On the first sign change of Fourier coefficients of cusp forms

abstract: We present a variant of the current widely-used method initiated by Choie and Kohnen in the study of the location of the first sign change of the Fourier coefficients of a holomorphic cusp form when all the coefficients are real. This version circumvents the use of Atkin-Lehner theory of cuspidal newforms, instead utilizing the Eisenstein series, and it applies directly to cases including integral weight cusp forms on the congruence subgroup $\Gamma_0(N)$ of any level $N$ as well as half-integral weight cusp forms.