A short note on inadmissible coefficients of weight 2 and $$2k+1$$ newforms

Abstract

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.