On some first sign change problems of modular forms

Abstract

We give two different bounds, namely, for the first prime p such that the p -th Hecke eigenvalue λ f ( p ) is negative when f is a normalized cuspidal newform of level Γ 0 ( N ) , and for the first sign change for general cusp forms, which improves the bound given by Choie and Kohnen [3] in the level aspect in the case of prime level.