def module(self):
"""
Return the underlying free module corresponding to this space
of modular forms.
If the dimension of self can be computed reasonably quickly,
then this function returns a free module (viewed as a tuple
space) of the same dimension as self over the same base ring.
Otherwise, the dimension of self.module() may be smaller. For
example, in the case of weight 1 forms, in some cases the
dimension can't easily be computed so self.module() is of
smaller dimension.
EXAMPLES::
sage: m = ModularForms(Gamma1(13),10)
sage: m.free_module()
Vector space of dimension 69 over Rational Field
sage: ModularForms(Gamma1(13),4, GF(49,'b')).free_module()
Vector space of dimension 27 over Finite Field in b of size 7^2
Note that in the following example the dimension can't be
(quickly) computed, so M.module() returns a space of different
dimension than M::
sage: M = ModularForms(Gamma1(57), 1); M
Modular Forms space of dimension (unknown) for Congruence ...
sage: M.module()
Vector space of dimension 36 over Rational Field
sage: M.basis()
Traceback (most recent call last):
...
NotImplementedError: Computation of dimensions of weight 1 cusp forms spaces not implemented in general
"""
if hasattr(self, "__module"): return self.__module
try:
d = self.dimension()
except NotImplementedError:
# This only comes up for weight 1 forms, where we want to be able
# to embed Eisenstein forms (which we know how to calculate) into
# some suitable ambient space. Because we can't even calculate the
# dimension of the weight 1 cusp forms in general, we just map
# Eisenstein series onto basis vectors, and then make it clear by
# raising errors in appropriate places that some cusp forms might
# exist but we don't know how to compute them.
d = self._dim_eisenstein()
self.__module = free_module.VectorSpace(self.base_ring(), d)
return self.__module
def module(self):
"""
Return the underlying free module corresponding to this space
of modular forms.
EXAMPLES::
sage: m = ModularForms(Gamma1(13),10)
sage: m.free_module()
Vector space of dimension 69 over Rational Field
sage: ModularForms(Gamma1(13),4, GF(49,'b')).free_module()
Vector space of dimension 27 over Finite Field in b of size 7^2
"""
d = self.dimension()
return free_module.VectorSpace(self.base_ring(), d)