2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63042We define the counting function for non-analytic (Maass) newforms of Hecke congruence groups_Gamma_0(M)_. We then calculate the three main terms of this counting function and give necessary and sufficient conditions on M for this counting function to have the same shape as if it were counting eigenvalues related to a cocompact group.Number TheorySpectral Theory11F12 (Primary) 11F72, 11F25 (Secondary)text