Computing the Fourier coefficients of modular forms is an important problem in computational number theory. In this talk we give some evidence that this task is likely to be hard. In particular, we show that computing the Fourier coefficients of any fixed Hecke eigenform is at least as hard as factoring integers of the form pq (where p and q are distinct primes). We will also discuss the consequence of this result to the problem of computing a basis of modular forms. This is joint work with Eric Bach.