First sign changes of modular forms for general level N

Abstract

Let f(z) = En>0 a(n)qn be a cusp form of weight k on Gamma 0(N) with real Fourier coefficients a(n). When N is squarefree, Choie and Kohnen gave a bound that the first sign change of a(n) occurs, and recently it was improved by He and Zhao. In this paper, we compute a bound for the first sign change problem for arbitrary N.(c) 2023 Elsevier Inc. All rights reserved.