7.2.1.3 ModularForms Objects

class ModularForms
An ambient space of modular forms. Create using the command

ModularForms(weight, group, character)

INPUT: group - a congruence subgroup (sage.modular.congroup.CongruenceSubgroup) weight - an integer base_field - a field (default rings.RationalField)

ModularForms( group, weight, [base_field=Rational Field])

Instances of class ModularForms have the following methods (in addition to inherited methods and special methods):

ambient_space,$  $ change_base,$  $ cuspidal_subspace,$  $ dim_cuspidal,$  $ dim_eisenstein,$  $ dim_new_cuspidal,$  $ dim_new_eisenstein,$  $ dimension,$  $ eisenstein_params,$  $ eisenstein_series,$  $ eisenstein_subspace,$  $ is_ambient,$  $ modular_symbols,$  $ new_subspace,$  $ prec,$  $ qexp,$  $ vector_space

These methods are defined as follows:

ambient_space( )

change_base( F)

cuspidal_subspace( )

dim_cuspidal( )

dim_eisenstein( )

dim_new_cuspidal( )

dim_new_eisenstein( )

dimension( )

eisenstein_params( )

eisenstein_series( )

eisenstein_subspace( )

is_ambient( )

modular_symbols( )

new_subspace( )

prec( [set=None])

Set or get default initial precision for printing modular forms.

qexp( vector, prec)

Compute the $ q$ -expansion to precision prec of the linear combination of the basis for this space given by the vector.

vector_space( )

See About this document... for information on suggesting changes.