A converse theorem for $\Gamma_0(13)$
  We 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 $\Gamma_0(13)$. 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. 
J.B. Conrey, David W. Farmer, B.E. Odgers, and N.C. Snaith