2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118195We specialize the Eichler-Selberg trace formula to obtain trace formulas for the prime-to-level Hecke action on cusp forms for certain congruence groups of arbitrary level. As a consequence, we determine the asymptotic in the prime p of the number of (weighted) SL(2,Z)-conjugation orbits of 2 by 2 matrices of determinant p whose reductions modulo N lie in a given conjugacy class in GL(2,Z/NZ). This generalizes an 1885 result of Hurwitz.21 pagesNumber Theory11R29; 11F32text