Package sage :: Package modular :: Package modform :: Module modform :: Class ModularForms
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Type ModularForms

  HeckeModule --+    
                |    
ModularFormsSpace --+
                    |
       object --+   |
                |   |
_uniqModularForms --+
                    |
                   ModularForms

Known Subclasses:
ModularFormsWithCharacter

An ambient space of modular forms.  Create using the command

    ModularForms(weight, group, character)

INPUT:
    group -- a congruence subgroup (sage.modular.congroup.CongruenceSubgroup)
    weight -- an integer 
    base_field -- a field (default rings.RationalField)

Method Summary
  __init__(self, group, weight, base_field)
  __repr__(self)
  ambient_space(self)
  change_base(self, F)
  cuspidal_subspace(self)
  dim_cuspidal(self)
  dim_eisenstein(self)
  dim_new_cuspidal(self)
  dim_new_eisenstein(self)
  dimension(self)
  eisenstein_params(self)
  eisenstein_series(self)
  eisenstein_subspace(self)
  is_ambient(self)
  modular_symbols(self)
  new_subspace(self)
  prec(self, set)
Set or get default initial precision for printing modular forms.
  qexp(self, vector, prec)
Compute q-expansion to precision prec of the linear combination of the basis for this space given by the vector.
  vector_space(self)
    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 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)
  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.
  embedded_subspace(self)
  group(self)
  has_character(self)
  hecke_matrix(self, n)
  intersect(self, right)
  key(self)
  level(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)

Instance Method Details

prec(self, set=None)

Set or get default initial precision for printing modular forms.

qexp(self, vector, prec)

Compute q-expansion to precision prec of the linear combination of the basis for this space given by the vector.

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