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