Package sage :: Package modular :: Package modform :: Module modform :: Class ModularFormsSubspace
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Class ModularFormsSubspace

  HeckeModule --+    
                |    
ModularFormsSpace --+
                    |
                   ModularFormsSubspace


A subspace of an ambient space of modular forms.
Method Summary
  __init__(self, ambient_space, vector_space)
ambient_space -- ModularFormsSpace subspace -- a vector subspace of the underlying vector space of the ambient space.
  __repr__(self)
  ambient_space(self)
  change_base(self)
  dimension(self)
  is_ambient(self)
  vector_space(self)
    Inherited from ModularFormsSpace
  __add__(self, right)
  __and__(self, right)
  __call__(self, x, check)
  __cmp__(self, x)
  __contains__(self, x)
True if x is an element or subspace of self.
  base_field(self)
  basis(self)
  character(self)
  cuspidal_subspace(self)
  decompose(self)
This function returns a list of subspaces V(f_i,t) corresponding to newforms f_i of some level dividing the level of self, such that the direct sum of the subspaces equals self, if possible.
  eisenstein_subspace(self)
  embedded_subspace(self)
  group(self)
  has_character(self)
  hecke_matrix(self, n)
  intersect(self, right)
  key(self)
  level(self)
  modular_symbols(self)
  newspaces(self)
This function returns a list of subspaces S(M,t) and E(M,t), corresponding to levels M dividing N and integers t dividing N/M, such that self is the direct sum of these spaces, if possible.
  sturm_bound(self, M)
For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B.
  weight(self)
    Inherited from HeckeModule
  base_ring(self)
  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)

Method Details

__init__(self, ambient_space, vector_space)
(Constructor)

ambient_space -- ModularFormsSpace subspace -- a vector subspace of the underlying vector space of the ambient space.
Overrides:
sage.modular.modform.modform.ModularFormsSpace.__init__

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