The GAP package Congruence provides functions to construct several types of canonical congruence subgroups in SL_2(Z), and also intersections of a finite number of such subgroups.
Furthermore, it implements the algorithm for generating Farey symbols for congruence subgroups and using them to produce a system of independent generators for these subgroups.
Congruence does not use external binaries and, therefore, works without restrictions on the type of the operating system. It is redistributed with GAP, but is not loaded by default. Therefore, to use Congruence, first you need to load it using the following command:
Ann Dooms, Eric Jespers, Alexander Konovalov, Helena Verrill