Package sage :: Package modular :: Package modsym :: Module ambient :: Class ModularSymbolsAmbient_wt2_g0_Q
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Type ModularSymbolsAmbient_wt2_g0_Q

                  Gens --+            
                         |            
           HeckeModule --+            
                         |            
       ModularSymbolsSpace --+        
                             |        
                object --+   |        
                         |   |        
_uniqModularSymbolsAmbient --+        
                             |        
         ModularSymbolsAmbient --+    
                                 |    
    ModularSymbolsAmbient_wtk_g0_Q --+
                                     |
                                    ModularSymbolsAmbient_wt2_g0_Q


Method Summary
  __init__(self, N, sign)
Initialize a space of modular symbols.
    Inherited from ModularSymbolsAmbient_wtk_g0_Q
  __repr__(self)
  manin_symbols(self)
    Inherited from ModularSymbolsAmbient
  __add__(self, other)
  __call__(self, x)
Coerce x into the modular symbols space.
  __getitem__(self, n)
  __len__(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.
  boundary_map(self)
The boundary map to the corresponding space of boundary modular symbols.
  commit(self)
Try to commit this modular symbols space to the database.
  compute_presentation(self)
  cuspidal_subspace(self)
The cuspidal subspace.
  degeneracy_map(self, level, t)
The t-th degeneracy map from self to modular symbols of the given level.
  dimension(self)
Returns the dimension of self.
  eisenstein_subspace(self)
  element(self, x)
Creates and returns an element of self from a modular or sage symbol, if possible.
  embedded_subspace(self)
Returns the vector subspace of the vector space of the ambient space that defines self as a subspace of modular symbols.
  fcp(self, n)
Returns the factorization of the characteristic polynomial of the Hecke operator T_n of index n.
  filename(self)
Returns the filename of self that should be used to store self in the database.
  hecke_algebra(self)
Returns the Hecke algebra associated to self.
  intersect(self, other)
Returns the intersection of self and other, which must both lie in a common ambient space of modular symbols.
  is_ambient(self)
Returns true if and only if self is an ambient space of modular symbols, i.e., created by specifying a group, weight, character, and sign, and not by using a decomposition or other command.
  is_cuspidal(self)
  is_eisenstein(self)
  is_new(self, p)
  is_subspace(self, V)
Returns True if and only if self is a subspace of V.
  load(self)
Try to load the ambient space self from the database.
  manin_basis(self)
  manin_generators(self)
  manin_gens_to_basis(self)
  manin_relations(self)
  manin_symbols_basis(self)
A list of Manin symbols that form a basis for the ambient space self.
  new_subspace(self, p)
Returns the new or p-new subspace of self.
  p1list(self)
  relation_matrix(self)
  use_db(self)
Returns true if self is loaded and saved to disk.
  zero_subspace(self)
Returns the subspace of this space of modular symbols.
    Inherited from object
  __delattr__(...)
x.__delattr__('name') <==> del x.name
  __getattribute__(...)
x.__getattribute__('name') <==> x.name
  __hash__(x)
x.__hash__() <==> hash(x)
  __reduce__(...)
helper for pickle
  __reduce_ex__(...)
helper for pickle
  __setattr__(...)
x.__setattr__('name', value) <==> x.name = value
  __str__(x)
x.__str__() <==> str(x)
    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_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.
  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)
  __getslice__(self, n, m)
  gens(self)
  list(self)

Instance Method Details

__init__(self, N, sign=0)
(Constructor)

Initialize a space of modular symbols.
INPUT:
    N -- int, the level
    sign -- int, either -1, 0, or 1
OUTPUT:
    The space of modular symbols of weight 2, trivial character,
    level N and given sign.
Overrides:
sage.modular.modsym.ambient.ModularSymbolsAmbient_wtk_g0_Q.__init__

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