# Arithmetic Subgroups of \(\SL_2(\ZZ)\)#

This chapter describes the basic functionality for finite index subgroups of the modular group \(\SL_2(\ZZ)\).

- Arithmetic subgroups, finite index subgroups of \(\SL_2(\ZZ)\)
- Arithmetic subgroups defined by permutations of cosets
- Elements of arithmetic subgroups
- Congruence arithmetic subgroups of \(\SL_2(\ZZ)\)
- Congruence subgroup \(\Gamma_H(N)\)
- Congruence subgroup \(\Gamma_1(N)\)
- Congruence subgroup \(\Gamma_0(N)\)
- Congruence subgroup \(\Gamma(N)\)
- The modular group \(\SL_2(\ZZ)\)
- Farey symbol for arithmetic subgroups of \(\PSL_2(\ZZ)\)
- Helper functions for congruence subgroups