11.1.1.2 HeckeModule_generic Objects

class HeckeModule_generic
A very general Hecke module.

All Hecke module classes derive from this class--spaces of modular symbols (free modules), modular forms (finite-rank free modules), modular abelian varieties (infinitely divisible groups), torsion submodules of abelian varieties (finite groups), etc.

HeckeModule_generic( base_ring, level)

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

anemic_hecke_algebra,$  $ base_ring,$  $ category,$  $ character,$  $ dimension,$  $ hecke_algebra,$  $ is_full_hecke_module,$  $ is_hecke_invariant,$  $ level,$  $ submodule

Further documentation:

anemic_hecke_algebra( )

Return the Hecke algebra associated to this Hecke module.

sage: T = ModularSymbols(1,12).hecke_algebra()
sage: A = ModularSymbols(1,12).anemic_hecke_algebra()
sage: T == A
False
sage: A
Anemic Hecke algebra acting on Full Modular Symbols space for Gamma_0(1) of
weight 12 with sign 0 and dimension 3 over Rational Field
sage: A.is_anemic()
True

hecke_algebra( )

Return the Hecke algebra associated to this Hecke module.

sage: T = ModularSymbols(Gamma1(5),3).hecke_algebra()
sage: T
Full Hecke algebra acting on Full Modular Symbols space for Gamma_1(5) of
weight 3 with sign 0 and dimension 4 over Rational Field
sage: T.is_anemic()
False

is_full_hecke_module( )

Return True if this space is invariant under all Hecke operators.

is_hecke_invariant( n)

Return True if self is invariant under the Hecke operator $ T_n$ .

level( )

Returns the level of this modular symbols space.

INPUT:
   ModularSymbols self -- an arbitrary space of modular symbols
   
OUTPUT:
   int -- the level

sage: m = ModularSymbols(20)
sage: m.level()
20

Instances of class HeckeModule_generic also have the following special methods:

__cmp__

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