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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. 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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. 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