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Newforms, inner twists, and the inverse Galois problem for projective linear groups

Luis V. Dieulefait — 2001

Journal de théorie des nombres de Bordeaux

We reformulate more explicitly the results of Momose, Ribet and Papier concerning the images of the Galois representations attached to newforms without complex multiplication, restricted to the case of weight 2 and trivial nebentypus. We compute two examples of these newforms, with a single inner twist, and we prove that for every inert prime greater than 3 the image is as large as possible. As a consequence, we prove that the groups PGL ( 2 , 𝔽 2 ) for every prime ( 3 , 5 ( mod 8 ) , > 3 ) , and PGL ( 2 , 𝔽 5 ) for every prime ¬ 0 ± 1 ( mod 11 ) ; > 3 ) , are Galois groups...

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