Divisibility properties of subgroup numbers for the modular group. (Q2581074)

Let \(\text{PSL}(2,\mathbb{Z})\) denote the modular group. It is the mostly studied discrete group. Newman showed that all subgroups of the modular group having index greater than 6 are of index divisible by 6 and are all free. Let \(s_n\) denote the number of index \(n\) subgroups in \(\text{PSL}(2,\mathbb{Z})\) and \(f_\lambda\) denote the number of free subgroups in \(\text{PSL}(2,\mathbb{Z})\) of index \(6\lambda\). In this paper, the authors generalize the divisibility results for \(f_\lambda\) and \(s_n\) to congruences modulo higher powers of 2.