Newforms, inner twists, and the inverse Galois problem for projective linear groups
Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 2, pp. 395-411.

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(mod8),>3), and PGL(2,𝔽 5 ) for every prime ¬0±1(mod11);>3), are Galois groups over .

Nous reformulons de manière plus explicite les résultats de Momose, Ribet et Papier sur les images des représentations galoisiennes attachées à des newforms sans multiplication complexe, en nous restreignant aux formes de poids 2 et de caractère trivial. Nous calculons deux tels exemples de newforms, possédant une unique tordue conjuguée à la forme, et nous démontrons que pour tout nombre premier >3, l’image est aussi grosse que possible. Nous utilisons ce résultat pour prouver que les groupes PGL(2,𝔽 2 )(3,5(mod8),>3) et PGL(2,𝔽 5 )(¬0±1(mod11);>3) sont groupes de Galois sur .

@article{JTNB_2001__13_2_395_0,
     author = {Dieulefait, Luis V.},
     title = {Newforms, inner twists, and the inverse Galois problem for projective linear groups},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {2},
     year = {2001},
     pages = {395-411},
     zbl = {0996.11042},
     mrnumber = {1879665},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2001__13_2_395_0/}
}
Dieulefait, Luis V. Newforms, inner twists, and the inverse Galois problem for projective linear groups. Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 2, pp. 395-411. https://jtnb.centre-mersenne.org/item/JTNB_2001__13_2_395_0/

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