On modular mod ℓ Galois representations with exceptional images

✍ Scribed by Ian Kiming; Helena A. Verrill

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 387 KB
• Volume: 110
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.05.003

✦ Synopsis

We give a parametrization of the possible Serre invariants ðN; k; nÞ of modular mod c Galois representations of the exceptional types A 4 ; S 4 ; A 5 ; in terms of local data attached to the fields cut out by the associated projective representations. We show how this result combined with certain global considerations leads to an effective procedure that will determine for a given eigenform f and prime c whether a mod c representation attached to f is exceptional. We illustrate with numerical examples.