27.4 Subspace of ambient spaces of modular symbols

Module: sage.modular.modsym.subspace

Class: ModularSymbolsSubspace

class ModularSymbolsSubspace
Subspace of ambient space of modular symbols
ModularSymbolsSubspace( self, ambient_hecke_module, submodule, [dual_free_module=True], [check=None])

Functions: boundary_map,$  $ cuspidal_submodule,$  $ dual_star_involution_matrix,$  $ eisenstein_subspace,$  $ factorization,$  $ hecke_bound,$  $ is_cuspidal,$  $ is_eisenstein,$  $ star_involution

boundary_map( self)

The boundary map to the corresponding space of boundary modular symbols. (This is the restriction of the map on the ambient space.)

cuspidal_submodule( self)

Return the cuspidal subspace of this space of modular symbols.

dual_star_involution_matrix( self)

Return the matrix of the dual star involution, which is induced by complex conjugation on the linear dual of modular symbols.

eisenstein_subspace( self)

Return the Eisenstein subspace of this space of modular symbols.

factorization( self)

Returns a list of pairs $ (S,e)$ where $ S$ is simple spaces of modular symbols and self is isomorphic to the direct sum of the $ S^e$ as a module over the anemic Hecke algebra adjoin the star involution.

ASSUMPTION: self is a module over the anemic Hecke algebra.

star_involution( self)

Return the star involution on self, which is induced by complex conjugation on modular symbols.

Special Functions: __cmp__,$  $ _compute_sign_subspace,$  $ _repr_

_compute_sign_subspace( self, sign, [compute_dual=True])

Return the subspace of self that is fixed under the star involution.

INPUT:
    sign -- int (either -1 or +1)
    compute_dual -- bool (default: True) also compute dual subspace.
                    This are useful for many algorithms.
OUTPUT:
    subspace of modular symbols

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