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

Abstract Let $$f(z)=q+\sum _{n\ge 2}a(n)q^n$$ f(z)=q+∑n≥2a(n)qn be a weight k normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir Hong in (On L-functions modular elliptic curves certain K3 surfaces, Ramanujan J, 2021) for $$k=2$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">k=2 by ruling out or locating all odd prime values $$|\ell |<100$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">|ℓ|<100 their Fourier ( n ) when satisfies some congruences. also study case weights $$k\ge 1$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">k≥1 newforms where nebentypus is given quadratic Dirichlet character.