8.4.1.4 ModularSymbolsAmbient_wtk_g0_Q Objects

class ModularSymbolsAmbient_wtk_g0_Q
Modular symbols for Gamma_0(N) of integer weight k > 2 over the field Q.
ModularSymbolsAmbient_wtk_g0_Q( 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

Instances of class ModularSymbolsAmbient_wtk_g0_Q have the following functions (in addition to inherited functions and special functions):

boundary_space,$  $ manin_symbols,$  $ modular_symbols_of_level,$  $ modular_symbols_of_sign,$  $ modular_symbols_of_weight

Further documentation:

modular_symbols_of_level( 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).

modular_symbols_of_sign( sign)

Returns a space of modular symbols with the same defining properties (weight, sign, etc.) as this space except with given sign.

modular_symbols_of_weight( k)

Returns a space of modular symbols with the same defining properties (weight, sign, etc.) as this space except with weight k.

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