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High Weight

Farmer and James (see [CF99] and [FJ02]) verified that the characteristic polynomials of a very impressive range of Hecke operators $ T_{p,k}$ on level one modular forms are irreducible.

Problem 1.3.1   Greatly extend the range of computation carried out by Farmer and James. For example, verify that $ T_2$ acts irreducibly on $ S_k(1)$ for all $ k\leq 4096$ .

William Stein 2006-10-20