Vanishing of Poincare series for congruence subgroups

We consider the problem of the vanishing of {P}oincar\'e series for congruence subgroups. Denoting by $P_{k,m,N}$ the {P}oincar\'e series of weight $k$ and index $m$ for the group $\Gamma_0(N)$, we show that for certain choices of parameters $k,m,N$, the {P}oincar\'e series does not vanish. Our methods improve on previous results of Rankin (1980) and Mozzochi (1989).