  We prove for L-function attached to an automorphic cusp form for the Hecke
congruence group $\Gamma_0(D)$, which is also an eigenfunction of all the Hecke
operators, that a positive proportion of its non-trivial zeros lie on the
critical line. This result extends the work of J.L. Hafner of 1983 where the
case of the full modular group is considered.
