  Let $f(z)=q+\sum_{n\geq 2}a(n)q^n$ be a weight $k$ normalized newform with
integer coefficients and trivial residual mod 2 Galois representation. We
extend the results of Amir and Hong in \cite{AH} for $k=2$ by ruling out or
locating all odd prime values $|\ell|<100$ of their Fourier coefficients $a(n)$
when $n$ satisfies some congruences. We also study the case of odd weights
$k\geq 1$ newforms where the nebentypus is given by a real quadratic Dirichlet
character.
