12.2.2.2 ModularSymbolsAmbient_wt2_g0_Q Objects

class ModularSymbolsAmbient_wt2_g0_Q
Modular symbols for Gamma_0(N) of integer weight 2 over the field Q.
ModularSymbolsAmbient_wt2_g0_Q( N, [sign=0])

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.

Instances of class ModularSymbolsAmbient_wt2_g0_Q have the following methods (in addition to inherited methods and special methods):

boundary_space

Instances of class ModularSymbolsAmbient_wt2_g0_Q also have the following special methods:

_compute_hecke_matrix_prime,$  $ _cuspidal_new_subspace_dimension_formula,$  $ _cuspidal_submodule_dimension_formula,$  $ _dimension_formula

Further documentation:

_compute_hecke_matrix_prime( p)

Compute and return the matrix of the p-th Hecke operator.

sage: m = ModularSymbols(37,2)
sage: m._compute_hecke_matrix_prime(2).charpoly()
x^5 + x^4 - 8*x^3 - 12*x^2

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