  In this article, we give evidence that computing Fourier coefficients of the
Hecke eigenforms for composite indices is no easier than factoring integers. In
particular, we show that the existence of a polynomial time algorithm that,
given n, computes the n-th Fourier coefficient of a (fixed) Hecke eigenform
implies that we can factor most RSA moduli (numbers that are products of two
distinct primes) in polynomial time.
