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Is there a way to lift a matrix in $Sl_2(\mathbb{Z}/N\mathbb{Z})$ to $SL_2(\mathbb{Z})$ for an arbitrary N ?

I found this algorithm : here

But it seems to work only when $N$ is prime. I think that the algorithm described in Shimura (which the implementation cited above is base on) works for arbitrary N. But I don't know how to modify the one above to make it work. Does anyone know how to do it.

Ultimately my goal is to iterate through a list of representatives of $SL_2(\mathbb{Z}/24\mathbb{Z})$ in $SL_2(\mathbb{Z})$ so if anyone knows how to it without the above I would be equally (in fact probably more) grateful.

Is there a way to lift a matrix in $Sl_2(\mathbb{Z}/N\mathbb{Z})$ to $SL_2(\mathbb{Z})$ for an arbitrary N ?

I found this algorithm : here

But it seems to work only when $N$ is prime. I think that the algorithm described in Shimura (which the implementation cited above is base on) works for arbitrary N. But I don't know how to modify the one above to make it work. Does anyone know how to do it.

Ultimately my goal is to iterate through a list of representatives of $SL_2(\mathbb{Z}/24\mathbb{Z})$ in $SL_2(\mathbb{Z})$ so if anyone knows how to it without the above I would be equally (in fact probably more) grateful.