Modular forms for \(\Gamma_0(N)\) over \(\QQ\)¶

class sage.modular.modform.ambient_g0.ModularFormsAmbient_g0_Q(level, weight)[source]¶

Bases: ModularFormsAmbient

A space of modular forms for \(\Gamma_0(N)\) over \(\QQ\).

cuspidal_submodule()[source]¶

Return the cuspidal submodule of this space of modular forms for \(\Gamma_0(N)\).

EXAMPLES:

Sage

sage: m = ModularForms(Gamma0(33),4)
sage: s = m.cuspidal_submodule(); s
Cuspidal subspace of dimension 10 of Modular Forms space of dimension 14
 for Congruence Subgroup Gamma0(33) of weight 4 over Rational Field
sage: type(s)
<class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_g0_Q_with_category'>

Python

>>> from sage.all import *
>>> m = ModularForms(Gamma0(Integer(33)),Integer(4))
>>> s = m.cuspidal_submodule(); s
Cuspidal subspace of dimension 10 of Modular Forms space of dimension 14
 for Congruence Subgroup Gamma0(33) of weight 4 over Rational Field
>>> type(s)
<class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_g0_Q_with_category'>

Sage Live

m = ModularForms(Gamma0(33),4)
s = m.cuspidal_submodule(); s
type(s)

eisenstein_submodule()[source]¶

Return the Eisenstein submodule of this space of modular forms for \(\Gamma_0(N)\).

EXAMPLES:

Sage

sage: m = ModularForms(Gamma0(389),6)
sage: m.eisenstein_submodule()
Eisenstein subspace of dimension 2 of Modular Forms space of dimension 163
 for Congruence Subgroup Gamma0(389) of weight 6 over Rational Field

Python

>>> from sage.all import *
>>> m = ModularForms(Gamma0(Integer(389)),Integer(6))
>>> m.eisenstein_submodule()
Eisenstein subspace of dimension 2 of Modular Forms space of dimension 163
 for Congruence Subgroup Gamma0(389) of weight 6 over Rational Field

Sage Live

m = ModularForms(Gamma0(389),6)
m.eisenstein_submodule()