[en] Mathematics - Number Theory ; 11F11 (Primary) 11F80 ; 11R32 ; 12F12 (Secondary)

[en] It is shown that Maeda's conjecture on eigenforms of level 1 implies that for every positive even d and every p in a density-one set of primes, the simple group PSL_2(F_{p^d}) occurs as the Galois group of a number field ramifying only at p.