Abstract
Let f be a Maass eigenform that is a new form of level N on Γ0(N), with Laplace eigenvalue 1/4 + νf2. Then, all its Fourier coefficients {λf(n)}n=1∞ are real, and we may normalize so that λf(1) = 1. It is proved, in this paper, that the first sign change in the sequence {λf(n)}n=1∞ occurs at some n satisfying n ≪ {(3+|νf|2)N}1/2−δ and (n, N) = 1. This generalizes the previous results for holomorphic Hecke eigenforms.
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