Module: sage.modular.modform.submodule
Submodules of spaces of modular forms
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: ModularFormsSubmodule
self, 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
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
Functions: change_ring
self, base_ring) |
Return the base change of this subspace of modular forms to base_ring.
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.
Special Functions: __init__,
_compute_coefficients,
_compute_q_expansion_basis,
_repr_
self, element, X) |
Compute all coefficients of the modular form element in self for indices in X.
TODO: Implement this function.
sage: M = ModularForms(6,4).cuspidal_subspace() sage: M._compute_coefficients( M.basis()[0], range(1,100) ) Traceback (most recent call last): ... NotImplementedError
self, 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)]
self) |
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'
Class: ModularFormsSubmoduleWithBasis