2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210753We give the best possible lower bounds in order of magnitude for the number of positive and negative Hecke eigenvalues. This improves upon a recent work of Kohnen, Lau & Shparlinski. Also, we study an analogous problem for short intervals.to appear in Math. ZNumber Theory11F30, 11N25text