8.6.2.5 ManinSymbolList_gamma1 Objects

class ManinSymbolList_gamma1
List of Manin symbols for Gamma0(N).

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_gamma1( level, weight)

Instances of class ManinSymbolList_gamma1 have the following functions (in addition to inherited functions and special functions):

apply,$  $ apply_I,$  $ apply_J,$  $ 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.
OUTPUT:
    a list of pairs (j, alpha_i), where each alpha_i is an
integer, 
    j is an integer (the j-th Manin symbol), and the sum
alpha_i*x_i 
    is the image of self 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_J( j)

Apply 2x2 matrix J = [-1,0,0,-1].

apply_S( j)

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