Abstract

Let f be an even integral weight, normalized, cuspidal Hecke eigenform over SL2(Z) with Fourier coefficients a(n). Let j be a positive integer. We prove that for almost all primes p the sequence (a(p(jn)))(n >= 0) has infinitely many sign changes. We also obtain a similar result for any cusp form with real Fourier coefficients that provide the characteristic polynomial of some generalized Hecke operator is irreducible over Q.