  Iwaniec and Sarnak showed that at the minimum 25% of L-values associated to
holomorphic newforms of fixed even integral weight and level $N \rightarrow
\infty$ do not vanish at the critical point when N is square-free and
$\phi(N)\sim N$. In this paper we extend the given result to the case of prime
power level $N=p^{\nu}$, $\nu\geq 2$.
