We consider some questions related to the signs of Hecke eigenvalues
or Fourier coecients of classical modular forms. One problem is to determine to
what extent those signs, for suitable sets of primes, determine uniquely the modular
form, and we give both individual and statistical results. The second problem, which
has been considered by a number of authors, is to determine the size, in terms of
the conductor and weight, of the rst sign-change of Hecke eigenvalues. Here we
improve the recent estimate of Iwaniec, Kohnen and Sengupta.