CoCalc -- modularform

Harvard Workshop: Distribution of modular symbols and L-values
code / alex / psage / psage / modform / fourier_expansion_framework / modularforms / modularform_ambient.py
²⁴¹⁸⁵² views
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r"""
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Rings of orthogonal modular forms.
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AUTHOR :
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    -- Martin Raum (2009 - 07 - 30) Initial version
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"""
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#===============================================================================
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# 
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# Copyright (C) 2009 Martin Raum
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# 
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# This program is free software; you can redistribute it and/or
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# modify it under the terms of the GNU General Public License
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# as published by the Free Software Foundation; either version 3
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# of the License, or (at your option) any later version.
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# 
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# This program is distributed in the hope that it will be useful, 
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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# General Public License for more details.
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# 
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# You should have received a copy of the GNU General Public License
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# along with this program; if not, see <http://www.gnu.org/licenses/>.
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#
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#===============================================================================
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from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_module import GradedExpansionModule_class
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from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_ring import GradedExpansionRing_class
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from psage.modform.fourier_expansion_framework.modularforms.modularform_element import ModularForm_generic
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from psage.modform.fourier_expansion_framework.modularforms.modularform_functor import ModularFormsFunctor
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from psage.modform.fourier_expansion_framework.modularforms.modularform_interfaces import ModularFormsAmbientWithHeckeAction_abstract
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from psage.modform.fourier_expansion_framework.modularforms.modularform_submodule import ModularFormsWeightSubmodule
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from sage.rings.integer import Integer
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from sage.rings.integer_ring import ZZ
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from sage.structure.element import Element
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#===============================================================================
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# ModularFormsAmbient
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#===============================================================================
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def ModularFormsAmbient( A, type, precision, *args, **kwds) :
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    """
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    Create a ring or module of modular forms of given type.  The underlying Fourier
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    expansions are calculated up to ``precision``.
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    INPUT:
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        - `A`             -- A ring; The base ring for the modular forms.
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        - ``type``        -- An inystance of :class:~`fourier_expansion_framework.modularforms.modularform_types.ModularFormType_abstract`.
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        - ``precision``   -- A precision class.
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        - ``*arg``        -- Will be forwarded to the type's construction function.
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        - ``**kwds``      -- Will be forwarded to the type's construction function.
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    OUTPUT:
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        An instance of :class:~`ModularFormsAmbient_abstract`.
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    TESTS::
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        sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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        sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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        sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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        sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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        sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_vectorvalued(), NNFilter(5), reduce_before_evaluating = False )
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    """
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    if not 'reduce_before_evaluating' in kwds :
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        kwds['reduce_before_evaluating'] = type.reduce_before_evaluating(A)
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    return type._ambient_construction_function()(A, type, precision, *args, **kwds)    
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#===============================================================================
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# ModularFormsAmbient_abstract
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#===============================================================================
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class ModularFormsAmbient_abstract :
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    """
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    An abstract implementation of a graded expansion ambient, that deduced its structure from
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    data stored by a type of modular forms.
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    """
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    def __init__(self, type, precision) :
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        """
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        INPUT:
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            - ``type``        -- An inystance of :class:~`fourier_expansion_framework.modularforms.modularform_types.ModularFormType_abstract`.
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            - ``precision``   -- A precision class.
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        NOTE:
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            - The attribute ``_extended_base_ring`` must be set before calling the constructor or 
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              will be ignored.
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            - The attribute ``_submodule_classes`` will be overwritten and has to be populated after calling the
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              constructor. See :meth:~`._submodule` for its description.
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            - The attribute ``_element_class`` may not be set if it has to be adopted from the type. 
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient_abstract( ModularFormTestType_scalar(), NNFilter(5) )        
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        """
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        self.__type = type
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        self.__precision = precision
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        if not hasattr(self, '_element_class') :
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            try :
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                self._element_class = type._ambient_element_class()
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            except NotImplementedError :
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                self._element_class = ModularForm_generic
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        single_weight_pred = lambda basis, **kwds: "grading_indices" in kwds and len(kwds["grading_indices"]) == 1
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        def single_weight_function(basis, **kwds) :
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            try :
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                return self.__type._weight_submodule_class()(self, basis, kwds["grading_indices"][0], **kwds)
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            except NotImplementedError :
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                return ModularFormsWeightSubmodule(self, basis, kwds["grading_indices"][0]) 
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        self._submodule_classes = [( single_weight_pred, single_weight_function ),
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                                   ( lambda _, **kwds : True,
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                                     lambda basis, **kwds : self._graded_ambient_class._submodule(self, basis, **kwds) ) ]
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#   This couldn't be refactored completely and will most likely cause problems in the 
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#   the concrete implementations. A complete replacement has taken place and this is
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#   probably no issue.
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#   def precision(self) :
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    def fourier_expansion_precision(self) :
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        """
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        The common precision of the underlying Fourier expansions.
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        OUTPUT:
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            A filter for the Fourier expansion ambient's monoid or action.
127
        
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient_abstract( ModularFormTestType_scalar(), NNFilter(5) )        
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            sage: ma.fourier_expansion_precision()
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            Filtered NN with action up to 5
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        """
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        return self.__precision
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    def type(self) :
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        """
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        The type of modular forms this ambient contains.
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        OUTPUT:
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            An instance of :class:~`fourier_expansion_framework.modularforms.modularform_types.ModularFormType_abstract`.
144
        
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient_abstract( ModularFormTestType_scalar(), NNFilter(5) )            
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            sage: ma.type()
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            Test type of modular forms with 5 generators
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        """
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        return self.__type
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    def group(self) :
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        """
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        The modular group the modular forms in this ambient are attached to.
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        OUTPUT:
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            An arbitrary type.
161
        
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient_abstract( ModularFormTestType_scalar(), NNFilter(5) )            
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            sage: ma.group()
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            '1'
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        """
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        return self.__type.group()
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    def weights(self) :
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        """
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        The generators' weights.
175
        
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        OUTPUT:
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            A tuple of (generalized) weights.
178
        
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: ma.weights()
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            (1, 2, 3, 4, 5)
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        """
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        return self.__type.weights(self.relations().base_ring())
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    def graded_submodules_are_free(self) :
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        """
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        Whether the modules of elements of fixed grading are free.
192
        
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        OUTPUT:
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            A boolean.
195
        
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: ma.graded_submodules_are_free()
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            True
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        """
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        return self.__type.graded_submodules_are_free(self.relations().base_ring())
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    def _submodule(self, basis, **kwds) :
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        """
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        A submodule with given basis.
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        INPUT:
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            - ``basis``  -- A list of elements of ``self``.
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            - ``**kwds`` -- Will be forwarded to the submodule construction function.
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        OUTPUT:
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            A submodule of graded expansions.
216
        
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: sm = ma._submodule([ma.0], grading_indices = [1])
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        """
224
        for pred, fcn in self._submodule_classes :
225
            if pred(basis, **kwds) : return fcn(basis, **kwds)
226
        
227
        raise RuntimeError, "submodule classes do not match %s, %s" % (basis, kwds)
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    def construction(self) :
230
        """
231
        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: (F, A) = ma.construction()
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            sage: F(A) == ma
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            True
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        """
240
        return ModularFormsFunctor(self.__type, self.__precision), self.relations().base_ring()
241

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    def _coerce_map_from_(self, other) :
243
        """
244
        TESTS::
245
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: ma2 = ModularFormsAmbient( ZZ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: ma._coerce_map_from_(ma2)
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            Conversion via _element_constructor_ map:
252
              From: Graded expansion ring with generators g1, g2, g3, g4, g5
253
              To:   Graded expansion ring with generators g1, g2, g3, g4, g5
254
        """
255
        from sage.structure.coerce_maps import CallableConvertMap
256
        
257
        if isinstance(other, ModularFormsAmbient_abstract) and \
258
           self.relations().base_ring().has_coerce_map_from(other.relations().base_ring()) and \
259
           self.type() == other.type() :
260
            return CallableConvertMap(other, self, self._element_constructor_)
261

262
        return self._graded_ambient_class._coerce_map_from_(self, other)
263

264
    def _element_constructor_(self, x) :
265
        """
266
        TESTS::
267
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
268
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
269
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
270
            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
271
            sage: ma2 = ModularFormsAmbient( ZZ, ModularFormTestType_scalar(), NNFilter(5) )
272
            sage: ma(ma2.0)
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            Graded expansion g1
274
        """
275
        if isinstance(x, (int, Integer)) and x == 0 :
276
            return self._element_class(self, self.relations().ring().zero())
277
        
278
        if isinstance(x, Element) :
279
            P = x.parent()
280
            if isinstance(P, ModularFormsAmbient_abstract) :
281
                if P.type() == self.type() and \
282
                   self.relations().base_ring().has_coerce_map_from(P.relations().base_ring()) :
283
                    return self._element_class( self,
284
                            self.relations().ring()( x.polynomial(). \
285
                              subs(self.type()._hom_base_extension(P.relations().base_ring(), self.relations().base_ring())) )
286
                           )
287

288
        return self._graded_ambient_class._element_constructor_(self, x)
289
    
290
    def __cmp__(self, other) :
291
        """
292
        TESTS::
293
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
294
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
295
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
296
            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: ma == ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
298
            True
299
            sage: ma == ModularFormsAmbient( ZZ, ModularFormTestType_scalar(), NNFilter(5) )
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            False
301
            sage: ma == ModularFormsAmbient( QQ, ModularFormTestType_vectorvalued(), NNFilter(5) )
302
            False
303
        """
304
        c = cmp(type(self), type(other)) 
305
        
306
        if c == 0 :
307
            c = cmp(self.type(), other.type())
308
        if c == 0 :
309
            c = cmp(self.relations().base_ring(), other.relations().base_ring())
310
        
311
        return c
312
    
313
#===============================================================================
314
# ModularFormsRing_generic
315
#===============================================================================
316

317
class ModularFormsRing_generic ( ModularFormsAmbient_abstract, GradedExpansionRing_class ) :
318
    def __init__(self, K, type, precision, **kwds) :
319
        """
320
        INPUT:
321
            - `K`             -- A ring.
322
            - ``type``        -- An inystance of :class:~`fourier_expansion_framework.modularforms.modularform_types.ModularFormType_abstract`.
323
            - ``precision``   -- A precision class.
324
            - ``**kwds``      -- Will be forwardd to :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_ring.GradedExpansionRing_class`.
325
        
326
        NOTE:
327
            - The attribute ``_extended_base_ring`` must be set before calling the constructor or 
328
              will be ignored.
329
            - The attribute ``_graded_ambient_class`` may not be set.
330
            - The attribute ``_submodule_classes`` will be overwritten and has to be populated after calling the
331
              constructor. See :meth:~`fourier_expansion_framework.modularforms.modularform_ambient._submodule` for its description.
332
            - The attribute ``_element_class`` may not be set if it has to be adopted from the type. 
333
        
334
        TESTS::
335
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
336
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
337
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
338
            sage: ma = ModularFormsRing_generic( QQ, ModularFormTestType_scalar(), NNFilter(5) )
339
            sage: ma.has_coerce_map_from(QQ)
340
            True    
341
        """
342
        if not hasattr(self, '_extended_base_ring') :
343
            try :
344
                if type.is_vector_valued() :
345
                    nvv_type = type.non_vector_valued()
346
                    self._extended_base_ring = ModularFormsAmbient(K, nvv_type, precision)
347
            except NotImplementedError :
348
                del self._extended_base_ring
349
        
350
        if not hasattr(self, '_graded_ambient_class') :
351
            self._graded_ambient_class = GradedExpansionRing_class
352
        
353
        if not 'all_relations' in kwds :
354
            kwds['all_relations'] = True
355
            
356
        ModularFormsAmbient_abstract.__init__(self, type, precision)
357
        GradedExpansionRing_class.__init__(self, type.base_ring_generators(K, precision),
358
         type.generators(K, precision), type.generator_relations(K), type.grading(K), **kwds)
359

360
        #=======================================================================
361
        # self._populate_coercion_lists_(
362
        #  coerce_list = [GradedExpansionBaseringInjection(self.base_ring(), self)], 
363
        #  convert_list = [self.relations().ring()],
364
        #  convert_method_name = "_graded_expansion_submodule_to_graded_ambient_" )
365
        #=======================================================================
366
        
367
    def _coerce_map_from_(self, other):
368
        """
369
        TESTS::
370
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
371
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
372
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
373
            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
374
            sage: ma._coerce_map_from_(ma)
375
            Conversion via _element_constructor_ map:
376
              From: Graded expansion ring with generators g1, g2, g3, g4, g5
377
              To:   Graded expansion ring with generators g1, g2, g3, g4, g5
378
        """
379
        from sage.structure.coerce_maps import CallableConvertMap
380
        
381
        if isinstance(other, ModularFormsRing_generic) and \
382
           self.base_ring().has_coerce_map_from(other.base_ring()) and \
383
           self.type().is_vector_valued() and \
384
           self.type().non_vector_valued() == other.type() :
385
            return CallableConvertMap(other, self, self._element_constructor_)
386
        
387
        return ModularFormsAmbient_abstract._coerce_map_from_(self, other)
388

389
    def _element_constructor_(self, x) :
390
        """
391
        TESTS::
392
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
393
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
394
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
395
            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
396
            sage: ma2 = ModularFormsAmbient( ZZ, ModularFormTestType_scalar(), NNFilter(5) )
397
            sage: ma(ma2.0)
398
            Graded expansion g1
399
        """
400
        if isinstance(x, Element) :
401
            P = x.parent()
402
            if isinstance(P, ModularFormsRing_generic) :
403
                try :
404
                    if self.type().is_vector_valued() and \
405
                       self.type().non_vector_values() == P.type() and \
406
                       self.base_ring().has_coerce_map_from(P.base_ring()) :
407
                        if self.base_ring() != P.base_ring() :
408
                            from sage.categories.pushout import pushout
409
                            x = pushout(P, self.base_ring())(x)
410
                        
411
                        return self._element_class( self,
412
                                self.relations().ring()( x.polynomial(). \
413
                                 subs(self.type()._hom_to_vector_valued(self.base_ring())) )
414
                               )
415
                except NotImplementedError :
416
                    pass
417
                
418
        return ModularFormsAmbient_abstract._element_constructor_(self, x)
419

420
#===============================================================================
421
# ModularFormsModule_generic
422
#===============================================================================
423

424
class ModularFormsModule_generic ( ModularFormsAmbient_abstract, GradedExpansionModule_class ) :
425
    def __init__(self, K, type, precision, **kwds) :
426
        """
427
        INPUT:
428
            - `K`             -- A ring.
429
            - ``type``        -- An inystance of :class:~`fourier_expansion_framework.modularforms.modularform_types.ModularFormType_abstract`.
430
            - ``precision``   -- A precision class.
431
            - ``**kwds``      -- Will be forwardd to :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_ring.GradedExpansionRing_class`.
432
        
433
        NOTE:
434
            - The attribute ``_extended_base_ring`` must be set before calling the constructor or 
435
              will be ignored.
436
            - The attribute ``_graded_ambient_class`` may not be set.
437
            - The attribute ``_submodule_classes`` will be overwritten and has to be populated after calling the
438
              constructor. See :meth:~`fourier_expansion_framework.modularforms.modularform_ambient._submodule` for its description.
439
            - The attribute ``_element_class`` may not be set if it has to be adopted from the type. 
440
        
441
        TESTS::
442
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
443
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
444
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
445
            sage: ma = ModularFormsModule_generic( QQ, ModularFormTestType_vectorvalued(), NNFilter(5) )
446
        """
447
        if not hasattr(self, '_extended_base_ring') :
448
            try :
449
                if type.is_vector_valued() :
450
                    nvv_type = type.non_vector_valued()
451
                    self._extended_base_ring = ModularFormsAmbient(K, nvv_type, precision)
452
            except NotImplementedError :
453
                del self._extended_base_ring
454

455
        if not hasattr(self, '_graded_ambient_class') :
456
            self._graded_ambient_class = GradedExpansionModule_class
457
        
458
        if not 'all_relations' in kwds :
459
            kwds['all_relations'] = True
460
            
461
        ModularFormsAmbient_abstract.__init__(self, type, precision)
462
        GradedExpansionModule_class.__init__(self, type.base_ring_generators(K, precision),
463
         type.generators(K, precision), type.generator_relations(K), type.grading(K), **kwds)
464

465
        #=======================================================================
466
        # self._populate_coercion_lists_(
467
        #  convert_list = [self.relations().ring()],
468
        #  convert_method_name = "_graded_expansion_submodule_to_graded_ambient_" )
469
        #=======================================================================
470

471
#===============================================================================
472
# ModularFormsRing_withheckeaction
473
#===============================================================================
474

475
class ModularFormsRing_withheckeaction(ModularFormsAmbientWithHeckeAction_abstract, ModularFormsRing_generic ) :
476
    def __init__(self, K, type, precision, **kwds) :
477
        """
478
        INPUT:
479
            - `K`             -- A ring.
480
            - ``type``        -- An inystance of :class:~`fourier_expansion_framework.modularforms.modularform_types.ModularFormType_abstract`.
481
            - ``precision``   -- A precision class.
482
            - ``**kwds``      -- Will be forwardd to :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_ring.GradedExpansionRing_class`.
483
        
484
        NOTE:
485
            - The attribute ``_extended_base_ring`` must be set before calling the constructor or 
486
              will be ignored.
487
            - The attribute ``_graded_ambient_class`` may not be set.
488
            - The attribute ``_submodule_classes`` will be overwritten and has to be populated after calling the
489
              constructor. See :meth:~`fourier_expansion_framework.modularforms.modularform_ambient._submodule` for its description.
490
            - The attribute ``_element_class`` may not be set if it has to be adopted from the type. 
491
        
492
        TESTS::
493
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
494
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
495
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
496
            sage: ma = ModularFormsRing_generic( QQ, ModularFormTestType_scalar(), NNFilter(5) )    
497
        """
498
        ModularFormsRing_generic.__init__(self, K, type, precision, **kwds)
499
        ModularFormsAmbientWithHeckeAction_abstract.__init__(self, type)
500

501
#===============================================================================
502
# ModularFormsModule_withheckeaction
503
#===============================================================================
504

505
class ModularFormsModule_withheckeaction(ModularFormsAmbientWithHeckeAction_abstract, ModularFormsModule_generic ) :
506
    def __init__(self, K, type, precision, **kwds) :
507
        """
508
        INPUT:
509
            - `K`             -- A ring.
510
            - ``type``        -- An inystance of :class:~`fourier_expansion_framework.modularforms.modularform_types.ModularFormType_abstract`.
511
            - ``precision``   -- A precision class.
512
            - ``**kwds``      -- Will be forwardd to :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_ring.GradedExpansionRing_class`.
513
        
514
        NOTE:
515
            - The attribute ``_extended_base_ring`` must be set before calling the constructor or 
516
              will be ignored.
517
            - The attribute ``_graded_ambient_class`` may not be set.
518
            - The attribute ``_submodule_classes`` will be overwritten and has to be populated after calling the
519
              constructor. See :meth:~`fourier_expansion_framework.modularforms.modularform_ambient._submodule` for its description.
520
            - The attribute ``_element_class`` may not be set if it has to be adopted from the type. 
521
        
522
        TESTS::
523
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
524
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
525
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
526
            sage: ma = ModularFormsModule_withheckeaction( QQ, ModularFormTestType_vectorvalued(), NNFilter(5) )
527
        """
528
        ModularFormsModule_generic.__init__(self, K, type, precision, **kwds)
529
        ModularFormsAmbientWithHeckeAction_abstract.__init__(self, type)
530
        
531
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