CoCalc -- submodule.py

GitHub Repository: sagemath/sagelib
Path: blob/master/sage/modular/modform/submodule.py
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"""
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Submodules of spaces of modular forms
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EXAMPLES::
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    sage: M = ModularForms(Gamma1(13),2); M
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    Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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    sage: M.eisenstein_subspace()
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    Eisenstein subspace of dimension 11 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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    sage: M == loads(dumps(M))
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    True
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    sage: M.cuspidal_subspace()
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    Cuspidal subspace of dimension 2 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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"""
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#########################################################################
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#       Copyright (C) 2004--2006 William Stein <[email protected]>
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#
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#  Distributed under the terms of the GNU General Public License (GPL)
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#
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#                  http://www.gnu.org/licenses/
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#########################################################################
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import space
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import sage.modular.hecke.submodule
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class ModularFormsSubmodule(space.ModularFormsSpace,
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                            sage.modular.hecke.submodule.HeckeSubmodule):
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    """
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    A submodule of an ambient space of modular forms.
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    """
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    def __init__(self, ambient_module, submodule, dual=None, check=False):
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        """
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        INPUT:
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        - ambient_module -- ModularFormsSpace
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        - submodule -- a submodule of the ambient space.
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        - dual_module -- (default: None) ignored
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        - check -- (default: False) whether to check that the
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                   submodule is Hecke equivariant
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        EXAMPLES::
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          sage: M = ModularForms(Gamma1(13),2); M
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          Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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          sage: M.eisenstein_subspace()
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          Eisenstein subspace of dimension 11 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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        """
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        A = ambient_module
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        sage.modular.hecke.submodule.HeckeSubmodule.__init__(self, A, submodule, check=check)
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        space.ModularFormsSpace.__init__(self, A.group(), A.weight(),
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                                         A.character(), A.base_ring())
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    def _repr_(self):
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        """
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        EXAMPLES::
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          sage: ModularForms(Gamma1(13),2).eisenstein_subspace()._repr_()
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          'Eisenstein subspace of dimension 11 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field'
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        """
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        return "Modular Forms subspace of dimension %s of %s"%(self.dimension(), self.ambient_module())
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    def _compute_coefficients(self, element, X):
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        """
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        Compute all coefficients of the modular form element in self for
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        indices in X.
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        TODO: Implement this function.
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        EXAMPLES::
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            sage: M = ModularForms(6,4).cuspidal_subspace()
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            sage: M._compute_coefficients( M.basis()[0], range(1,100) )
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            Traceback (most recent call last):
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            ...
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            NotImplementedError
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        """
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        raise NotImplementedError
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    def _compute_q_expansion_basis(self, prec):
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        """
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        Compute q_expansions to precision prec for each element in self.basis().
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        EXAMPLES::
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            sage: M = ModularForms(Gamma1(13),2); M
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            Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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            sage: S = M.eisenstein_subspace(); S
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            Eisenstein subspace of dimension 11 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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            sage: S._compute_q_expansion_basis(5)
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            [1 + O(q^5),
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             q + O(q^5),
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             q^2 + O(q^5),
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             q^3 + O(q^5),
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             q^4 + O(q^5),
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             O(q^5),
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             O(q^5),
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             O(q^5),
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             O(q^5),
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             O(q^5),
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             O(q^5)]
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        """
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        A = self.ambient_module()
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        return [A._q_expansion(element = f.element(), prec=prec) for f in self.basis()]
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# TODO
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class ModularFormsSubmoduleWithBasis(ModularFormsSubmodule):
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    pass
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