12.2 Coset representatives

The explicit representation of fundamental domains of arithmetic quotients $ H/\Gamma$ can be determined from the cosets of $ \Gamma$ in $ SL_2(\mathbf{Z})$ . How are these cosets computed in Sage?

Here is an example of computing the coset representatives of $ SL_2(\mathbf{Z})/\Gamma_0(11)$ :

sage: G = Gamma0(11); G
Congruence Subgroup Gamma0(11)
sage: list(G.coset_reps())
[[1, 0, 0, 1], [0, -1, 1, 0], [1, 0, 1, 1], [1, 1, 1, 2], [1, 2, 1, 3], 
 [1, 3, 1, 4], [1, 4, 1, 5], [1, 5, 1, 6], [1, 6, 1, 7], [1, 7, 1, 8], 
 [1, 8, 1, 9], [1, 9, 1, 10]]

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