  The nilpotence order of the mod 2 Hecke operators.
  Let $\Delta=\sum_{m=0}^\infty q^{(2m+1)^2} \in F_2[[q]]$ be the reduction mod
2 of the $\Delta$ series. A modular form f modulo 2 of level 1 is a polynomial
in $\Delta$. If p is an odd prime, then the Hecke operator Tp transforms f in a
modular form Tp(f) which is a polynomial in $\Delta$ whose degree is smaller
than the degree of f, so that Tp is nilpotent. The order of nilpotence of f is
defined as the smallest integer g = g(f) such that, for every family of g odd
primes p1, p2, ..., pg, the relation Tp1Tp2... Tpg (f) = 0 holds. We show how
one can compute explicitly g(f); if f is a polynomial of degree d in $\Delta$,
one finds that g(f) << d^(1/2).
