denote the classical modular group, ie. the
group of 
matrices with integer coefficients with
determinant +1. Let N be a positive integer. We define
We let denote the classical modular group, ie. the
group of matrices with integer coefficients with
determinant +1. Let N be a positive integer. We define
A subgroup of 
is called a congruence subgroup of level
N if it contains 
. The most important congruence
subgroups are
