The first sign change of Fourier coefficients of cusp forms

Abstract

Let $f=\sum_{n>o} a(n)q^{n}, a(n)$ real, be an arbitrary nonzero cusp form of even integral weight $k\geq 2$ on $\Gamma_0(N),$ square free $N.$ We obtain an effective bound that the first sign change of $a(n)$ occurs.