8.6.2.4 ManinSymbolList_gamma0 Objects

class ManinSymbolList_gamma0
List of Manin symbols for Gamma0(N).

ManinSymbolList_gamma0(level, weight): INPUT: level - integer level weight - integer weight >= 2

EXAMPLE:

sage: m = ManinSymbolList_gamma0(5,2); m
Manin Symbol List of weight 2 for Gamma0(5)
sage: m.manin_symbol_list()
[(0,1), (1,0), (1,1), (1,2), (1,3), (1,4)]
sage: m = ManinSymbolList_gamma0(6,4); m
Manin Symbol List of weight 4 for Gamma0(6)
sage: len(m)
36
ManinSymbolList_gamma0( level, weight)

Instances of class ManinSymbolList_gamma0 have the following functions (in addition to inherited functions and special functions):

apply,$  $ apply_I,$  $ apply_S,$  $ apply_T,$  $ apply_TT,$  $ level,$  $ normalize

Further documentation:

apply( j, m)

Apply the matrix m=[a,b,c,d] to the j-th Manin symbol.

INPUT:
    j -- integer
    m = [a, b, c, d] a list of 4 integers, which defines a 2x2
matrix.
    
OUTPUT:
    list -- a list of pairs (j_i, alpha_i), where each alpha_i
    is a nonzero integer, j_i is an integer (the j_i-th Manin
    symbol), and the sum alpha_i*x_{j_i} is the image of the
    j-th Manin symbol under the right action of the matrix
    [a,b;c,d].  Here the right action of g=[a,b;c,d] on a
    Manin symbol [P(X,Y),(u,v)] is [P(aX+bY,cX+dY),(u,v)*g].

apply_I( j)

apply_S( j)

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