42.5 Modular Forms for $ \Gamma_0(N)$ over $ \mathbf{Q}$

Module: sage.modular.modform.ambient_g0

Modular Forms for $ \Gamma_0(N)$ over $ \mathbf{Q}$ .

TESTS:

sage: m = ModularForms(Gamma0(389),6)
sage: loads(dumps(m)) == m
True

Class: ModularFormsAmbient_g0_Q

class ModularFormsAmbient_g0_Q
A space of modular forms for Gamma_0(N) over QQ.
ModularFormsAmbient_g0_Q( self, level, weight)

Create a space of modular symbols for $ \Gamma_0(N)$ of given weight defined over $ \mathbf{Q}$ .

sage: m = ModularForms(Gamma0(11),4); m
Modular Forms space of dimension 4 for Congruence Subgroup Gamma0(11) of
weight 4 over Rational Field
sage: type(m)
<class 'sage.modular.modform.ambient_g0.ModularFormsAmbient_g0_Q'>

Functions: cuspidal_submodule,$ \,$ eisenstein_submodule

cuspidal_submodule( self)

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

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'>

eisenstein_submodule( self)

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

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

Special Functions: __init__

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