Projective Linear Groups as Galois Groups overQvia Modular Representations

✍ Scribed by Luis Dieulefait; Núria Vila

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 288 KB
• Volume: 30
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1999.0383

✦ Synopsis

We give an algorithm for the determination of the finitely many primes such that the image of the modular Galois representations attached to a weight 2 newform on Γ 0 (N ) without complex multiplication or inner twists may not be "as large as possible".

We apply the algorithm to suitable newforms and we obtain the realization of the groups PSL(2, F 2 ), PGL(2, F 3 ) and PSL(2, F 4 ) as Galois groups over Q for high density sets of primes.