Let W(z) = 1 + Ad ezmidr + AdCl ewrim+lM + . . . be a modular form of weight n for the full modular group. Then for every constant b there exists an n, = n,,(b) such that if d > n/6 b and n > n, , then one of A@, A,, ,..., has a negative real part. This implies that there is no even unimodular lattice in E”, for n > n, , having minimum nonzero squared length > n/12 b. A similar argument shows that there is no binary self-dual code of length n > n, having all weights divisible by 4 and minimum nonzero weight > n/6 6. A corresponding result holds for ternary codes.