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
class sage.modular.modform.submodule.ModularFormsSubmodule(ambient_module, submodule, dual=None, check=False)

A submodule of an ambient space of modular forms.

__init__(ambient_module, submodule, dual=None, check=False)

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
_compute_coefficients(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
_compute_q_expansion_basis(prec)

Compute q_expansions to precision prec for each element in self.basis().

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)]

_repr_()
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’
change_ring(base_ring)

Return the base change of this subspace of modular forms to base_ring.

EXAMPLES:
sage: M = ModularForms(6,4) ; M.cuspidal_subspace().change_ring(GF(3)) Traceback (most recent call last): ... NotImplementedError: Base change only currently implemented for ambient spaces.
class sage.modular.modform.submodule.ModularFormsSubmoduleWithBasis(ambient_module, submodule, dual=None, check=False)

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