There is one answer in the following paper, along with a nice bibliography of other techniques:
MR1343700 (96k:20100)MR1343700 (96k:20100) Hsu, Tim(1-PRIN) Identifying congruence subgroups of the modular group. (English summary) Proc. Amer. Math. Soc. 124 (1996), no. 5, 1351--1359.