  The question about modular forms have recently received a lot of attention;
concerning the non-vanishing of automorphic L-functions Michel, Kowalski and
Vanderkam proved (among others results) that there's positive proportion of
non-vanishing of primitives forms at the critical point. This result was proved
by these authors in the prime level case; on the othe hand, Iwaniec, Luo and
Sarnak showed the same result for the squarefree level case. In order to
understand the influence of the arithmetic shape of level forms in their
vanishing, this paper studies a generalisation to the primitives forms with
prime powers level.
