An Application of Maeda's Conjecture to the Inverse Galois Problem
  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. 
Gabor Wiese
math.NT