  We consider a variant of a question of N. Koblitz. For an elliptic curve
$E/\Q$ which is not $\Q$-isogenous to an elliptic curve with torsion, Koblitz
has conjectured that there exists infinitely many primes $p$ such that
$N_p(E)=#E(\F_p)=p+1-a_p(E)$ is also a prime. We consider a variant of this
question. For a newform $f$, without CM, of weight $k\geq 4$, on $\Gamma_0(M)$
with trivial Nebentypus $\chi_0$ and with integer Fourier coefficients, let
$N_p(f)=\chi_0(p)p^{k-1}+1-a_p(f)$ (here $a_p(f)$ is the $p^{th}$-Fourier
coefficient of $f$). We show under GRH and Artin's Holomorphy Conjecture that
there are infinitely many $p$ such that $N_p(f)$ has at most
$[5k+1+\sqrt{\log(k)}]$ distinct prime factors. We give examples of about
hundred forms to which our theorem applies.
