"""
Modular Forms over a Non-minimal Base Ring
"""
import ambient
from cuspidal_submodule import CuspidalSubmodule_R
from sage.rings.all import ZZ
class ModularFormsAmbient_R(ambient.ModularFormsAmbient):
def __init__(self, M, base_ring):
"""
Ambient space of modular forms over a ring other than QQ.
EXAMPLES::
sage: M = ModularForms(23,2,base_ring=GF(7)) ## indirect doctest
sage: M
Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(23) of weight 2 over Finite Field of size 7
sage: M == loads(dumps(M))
True
"""
self.__M = M
if M.character() is not None:
self.__R_character = M.character().change_ring(base_ring)
else:
self.__R_character = None
ambient.ModularFormsAmbient.__init__(self, M.group(), M.weight(), base_ring, M.character())
def modular_symbols(self,sign=0):
r"""
Return the space of modular symbols attached to this space, with the given sign (default 0).
TESTS::
sage: K.<i> = QuadraticField(-1)
sage: chi = DirichletGroup(5, base_ring = K).0
sage: L.<c> = K.extension(x^2 - 402*i)
sage: M = ModularForms(chi, 7, base_ring = L)
sage: symbs = M.modular_symbols()
sage: symbs.character() == chi
True
sage: symbs.base_ring() == L
True
"""
sign = ZZ(sign)
try:
return self.__modular_symbols[sign]
except AttributeError:
self.__modular_symbols = {}
except KeyError:
pass
M = self.__M.modular_symbols(sign).change_ring(self.base_ring())
self.__modular_symbols[sign] = M
return M
def _repr_(self):
"""
String representation for self.
EXAMPLES::
sage: M = ModularForms(23,2,base_ring=GF(7)) ## indirect doctest
sage: M._repr_()
'Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(23) of weight 2 over Finite Field of size 7'
sage: chi = DirichletGroup(109).0 ** 36
sage: ModularForms(chi, 2, base_ring = chi.base_ring())
Modular Forms space of dimension 9, character [zeta3] and weight 2 over Cyclotomic Field of order 108 and degree 36
"""
s = str(self.__M)
i = s.find('over')
if i != -1:
s = s[:i]
return s + 'over %s'%self.base_ring()
def _compute_q_expansion_basis(self, prec=None):
"""
Compute q-expansions for a basis of self to precision prec.
EXAMPLES:
sage: M = ModularForms(23,2,base_ring=GF(7))
sage: M._compute_q_expansion_basis(5)
[1 + 5*q^3 + 5*q^4 + O(q^5),
q + 6*q^3 + 6*q^4 + O(q^5),
q^2 + 5*q^3 + 6*q^4 + O(q^5)]
"""
if prec == None:
prec = self.prec()
if self.base_ring().characteristic() == 0:
B = self.__M.q_expansion_basis(prec)
else:
B = self.__M.q_integral_basis(prec)
R = self._q_expansion_ring()
return [R(f) for f in B]
def cuspidal_submodule(self):
r"""
Return the cuspidal subspace of this space.
EXAMPLE::
sage: C = CuspForms(7, 4, base_ring=CyclotomicField(5)) # indirect doctest
sage: type(C)
<class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_R_with_category'>
"""
return CuspidalSubmodule_R(self)
def change_ring(self, R):
r"""
Return this modular forms space with the base ring changed to the ring R.
EXAMPLE::
sage: chi = DirichletGroup(109, CyclotomicField(3)).0
sage: M9 = ModularForms(chi, 2, base_ring = CyclotomicField(9))
sage: M9.change_ring(CyclotomicField(15))
Modular Forms space of dimension 10, character [zeta3 + 1] and weight 2 over Cyclotomic Field of order 15 and degree 8
sage: M9.change_ring(QQ)
Traceback (most recent call last):
...
ValueError: Space cannot be defined over Rational Field
"""
if not R.has_coerce_map_from(self.__M.base_ring()):
raise ValueError, "Space cannot be defined over %s" % R
return ModularFormsAmbient_R(self.__M, R)
