N, k, [sign=0]) |
Initialize a space of modular symbols of weight k for Gamma_0(N), over Q.
For weight 2, it is faster to use ModularSymbols_wt2_g0_Q.
INPUT: N -- int, the level k -- integer weight >= 2. sign -- int, either -1, 0, or 1
sage: ModularSymbols(1,12) Full Modular Symbols space for Gamma_0(1) of weight 12 with sign 0 and dimension 3 over Rational Field sage: ModularSymbols(1,12, sign=1).dimension() 2 sage: ModularSymbols(15,4, sign=-1).dimension() 4 sage: ModularSymbols(6,6).dimension() 10 sage: ModularSymbols(36,4).dimension() 36
boundary_space,
manin_symbols,
modular_symbols_of_level
Further documentation:
N) |
Returns a space of modular symbols with the same defining properties (weight, sign, etc.) as this space except with the level N.
For example, if self is the space of modular symbols of weight 2 for Gamma_0(22), and level is 11, then this function returns modular symbols of weight 2 for Gamma_0(11).
sage: M = ModularSymbols(11) sage: M.modular_symbols_of_level(22) Full Modular Symbols space for Gamma_0(22) of weight 2 with sign 0 and dimension 7 over Rational Field sage: M = ModularSymbols(Gamma1(6)) sage: M.modular_symbols_of_level(12) Full Modular Symbols space for Gamma_1(12) of weight 2 with sign 0 and dimension 9 over Rational Field
Instances of class ModularSymbolsAmbient_wtk_g0_Q also have the following special methods:
__repr__,
_cuspidal_new_subspace_dimension_formula,
_cuspidal_submodule_dimension_formula,
_degeneracy_raising_matrix,
_dimension_formula
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