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
level, weight) |
apply,
apply_I,
apply_J,
apply_S,
apply_T,
apply_TT,
level,
normalize
Further documentation:
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].
j) |
j) |
Apply 2x2 matrix J = [-1,0,0,-1].
j) |
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