We show that, for every x exceeding some explicit bound depending only on k and N, there are at least C(k,N)x/log ¹⁷x positive and negative coefficients a(n) with n≤x in the Fourier expansion of any non-zero cuspidal Hecke eigenform of even integral weight k≥2 and squarefree level N that is a newform, where C(k,N) depends only on k and N. From this we deduce the existence of a sign change in a short interval.
Copyright 2008 Cambridge University Press. Article originally published in Journal of the Australian Mathematical Society, Vol. 85, Iss. 1, pp. 87-94. The original article can be found at http://dx.doi.org/10.1017/S1446788708000323