2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107658We prove that a Dirichlet series with a functional equation and Euler product of a particular form can only arise from a holomorphic cusp form on the Hecke congruence group $Γ_0(13)$. The proof does not assume a functional equation for the twists of the Dirichlet series. The main new ingredient is a generalization of the familiar Weil's lemma that played a prominent role in previous converse theorems.10 pages, LaTeXNumber Theory11F66text