Submodules of spaces of modular forms

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> M = ModularForms(Gamma1(Integer(13)),Integer(2)); M
Modular Forms space of dimension 13 for
 Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
>>> 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
>>> M == loads(dumps(M))
True
>>> 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

Sage Live

M = ModularForms(Gamma1(13),2); M
M.eisenstein_subspace()
M == loads(dumps(M))
M.cuspidal_subspace()

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

Bases: ModularFormsSpace, HeckeSubmodule

A submodule of an ambient space of modular forms.

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

Bases: ModularFormsSubmodule

Make live