List of coset representatives for $\Gamma_H(N)$ in ${\rm SL}_2(\ZZ)$

class sage.modular.modsym.ghlist.GHlist(group)

Bases: sage.structure.sage_object.SageObject

A class representing a list of coset representatives for $\Gamma_H(N)$ in ${\rm SL}_2(\ZZ)$.

list()

Return a list of vectors representing the cosets. Do not change the returned list!

EXAMPLES:

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(4,[])); L.list()
[(0, 1), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3), (2, 1), (2, 3), (3, 0), (3, 1), (3, 2), (3, 3)]

normalize(u, v)

Given a pair $(u,v)$ of integers, return the unique pair $(u', v')$ such that the pair $(u', v')$ appears in self.list() and $(u, v)$ is equivalent to $(u', v')$.

This will only make sense if ${\rm gcd}(u, v, N) = 1$; otherwise the output will not be an element of self.

EXAMPLES:

sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [17, 19])).normalize(17, 6)
(1, 6)
sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [7, 13])).normalize(17, 6)
(5, 6)
sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [5, 23])).normalize(17, 6)
(7, 18)