Counting elements of the congruence subgroup

We obtain asymptotic formulas for the number of matrices in the congruence subgroup $${\mathrm{\Gamma }}_0(Q)=\{A\in {\mathrm{S}\mathrm{L}}_2(\mathbb{Z}):c\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}Q)\},$$ which are of naive height at most $X$. Our result is uniform in a very broad range of values $Q$ and $X$.