  Two integral structures on the Q-vector space of modular forms of weight two
on X_0(N) are compared at primes p exactly dividing N. When p=2 and N is
divisible by a prime that is 3 mod 4, this comparison leads to an algorithm for
computing the space of weight one forms mod 2 on X_0(N/2). For p arbitrary and
N>4 prime to p, a way to compute the Hecke algebra of mod p modular forms of
weight one on Gamma_1(N) is presented, using forms of weight p, and, for p=2,
parabolic group cohomology with mod 2 coefficients.
  Appendix A is a letter from Mestre to Serre, of October 1987, where he
reports on computations of weight one forms mod 2 of prime level.
  Appendix B reports on an implementation for p=2 in Magma, using Stein's
modular symbols package, with which Mestre's computations are redone and
slightly extended.
