Package sage :: Package modular :: Module dims
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Module sage.modular.dims

Dimensions of spaces of modular forms
Function Summary
  c0(n)
  c1(n)
  CO_delta(r, p, N, eps)
  CO_nu(r, p, N, eps)
  CohenOesterle(eps, k)
  cXNp(n)
  dimension_cusp_forms(group, k)
The dimension of the space of cusp forms for the congruence subgroup group.
  dimension_cusp_forms_eps(eps, k)
The dimension of the space of cusp forms of weight k and character eps.
  dimension_cusp_forms_gamma0(N, k)
  dimension_cusp_forms_gamma1(N, k)
  dimension_eis(group, k)
The dimension of the space of eisenstein series for the given congruence subgroup.
  dimension_new_cusp_forms(eps, k, p)
Dimension of the new subspace of cusp forms of weight k and character eps.
  dimension_new_cusp_forms_gamma0(N, k, p)
Dimension of the p-new subspace of S_k(Gamma_0(N)).
  dimension_new_cusp_forms_gamma1(N, k, p)
Dimension of the p-new subspace of S_k(Gamma_1(N)).
  dimension_new_cusp_forms_group(group, k)
The dimension of the new space of cusp forms for the congruence subgroup group.
  eisen(p)
  g0(n)
  g1(n)
  gXNp(n, p)
  idxG0(n)
Index of Gamma_0(N) in SL_2(Z).
  idxG1(n)
Index of Gamma_1(N) in SL_2(Z).
  mu0(n)
  mu1(n)
  mu20(n)
  mu21(n)
  mu2XNp(n, p)
  mu30(n)
  mu31(n)
  mu3XNp(n, p)
  mumu(N)
  muXNp(n, p)
  S0(n, k)
  S1(n, k)
  ss0(n, p)
  ss1(n, p)

Function Details

dimension_cusp_forms(group, k=2)

The dimension of the space of cusp forms for the congruence subgroup group.

dimension_cusp_forms_eps(eps, k=2)

The dimension of the space of cusp forms of weight k and character
eps.

INPUT:
    eps -- a Dirichlet character
    k -- int, a weight >= 2.
OUTPUT:
    int -- the dimension

EXAMPLES:
    >>> from sage.modular.dirichlet import *
    >>> G = DirichletGroup(13)
    >>> e = G.gen()
    >>> e.order()
    12
    >>> dimension_cusp_forms_eps(e,2)
    0
    >>> dimension_cusp_forms_eps(e**2,2)
    1

dimension_eis(group, k=2)

The dimension of the space of eisenstein series for the given congruence subgroup.

dimension_new_cusp_forms(eps, k=2, p=0)

Dimension of the new subspace of cusp forms of weight k and character eps.

dimension_new_cusp_forms_gamma0(N, k=2, p=0)

Dimension of the p-new subspace of S_k(Gamma_0(N)). If p=0, dimension of the new subspace.

dimension_new_cusp_forms_gamma1(N, k=2, p=0)

Dimension of the p-new subspace of S_k(Gamma_1(N)). If p=0, dimension of the new subspace.

dimension_new_cusp_forms_group(group, k=2)

The dimension of the new space of cusp forms for the congruence subgroup group.

idxG0(n)

Index of Gamma_0(N) in SL_2(Z).

idxG1(n)

Index of Gamma_1(N) in SL_2(Z).

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