Package sage :: Package modular :: Package modsym :: Module subspace :: Class ModularSymbolsSubspace
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Class ModularSymbolsSubspace

           Gens --+    
                  |    
    HeckeModule --+    
                  |    
ModularSymbolsSpace --+
                      |
                     ModularSymbolsSubspace


Method Summary
  __init__(self, ambient_space, vector_space)
  __repr__(self)
  ambient_space(self)
  ambient_vector(self, v)
Given a vector v in self.vector_space(), return the corresponding vector in the ambient modular symbols space.
  dimension(self)
  embedded_vector_space(self)
  is_ambient(self)
    Inherited from ModularSymbolsSpace
  __cmp__(self, other)
Compare self and other.
  base_field(self)
  base_ring(self)
  basis(self)
Returns a basis for self.
  character(self)
  eigenvalue(self, n)
Returns an eigenvalue of T_n acting on self, where self must be new and non-splittable.
  eigenvalues(self)
Return a_n, psi, i, where a_n is the n-th eigenvalue, psi : Z --> V is a map and i:V-->K is an isomorphism of V with a number field (or Q), such that the composition iso(psi(n)) is the eigenvalue of the n-th Hecke operator acting on a fixed element of self (which must be new and non-splittable).
  gen(self, n)
The n-th generator of self.
  group(self)
Returns the group of this modular symbols space.
  hecke_algebra(self, anemic)
  hecke_matrix(self, n)
The matrix of the n-th Hecke operator acting on the basis for self.
  hecke_operator(self, n)
Returns the n-th Hecke operator as a Matrix Function.
  is_cuspidal(self)
  is_new(self)
  level(self)
Returns the level of this modular symbols space.
  ngens(self)
The number of generators of self.
  projection(self)
Return the projection map from the ambient space to self.
  qeigenform(self, prec)
Returns the q-expansion to precision prec of a newform associated to self, where self must be new, cuspidal, and non-splittable.
  sign(self)
Returns the sign of self.
  sturm_bound(self)
Returns the Sturm bound for this space of modular symbols.
  T(self, n)
Returns the n-th Hecke operator T_n.
  vector_space(self)
Returns the underlying vector space of self.
  weight(self)
Returns the weight of this modular symbols space.
    Inherited from HeckeModule
  decomposition(self, anemic)
  factor_number(self)
  is_splittable(self)
Returns true if and only if only it is possible to split off a nontrivial generalized eigenspace of self as the kernel of some Hecke operator.
  is_splittable_anemic(self)
Returns true if and only if only it is possible to split off a nontrivial generalized eigenspace of self as the kernel of some Hecke operator of index coprime to the level.
  set_factor_number(self, i)
    Inherited from Gens
  __getattr__(self, attrname)
  __getitem__(self, n)
  __getslice__(self, n, m)
  gens(self)
  list(self)

Method Details

ambient_vector(self, v)

Given a vector v in self.vector_space(), return the corresponding vector in the ambient modular symbols space.

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