An \(\widehat{A_4}\) extension of \({\mathbb{Q}}\) attached to a non-selfdual automorphic form on \(GL(3)\)
Clozel has conjectured that an algebraic automorphic representation of GL(n) over \({\mathbb{Q}}\) has attached to it a compatible system of \(\lambda\)- adic representations of Gal(\({\bar {\mathbb{Q}}}/{\mathbb{Q}})\). When the automorphic representation is not essentially-selfdual no approaches to prove the conjecture or even examples of it are known. We provide modular numerical evidence for the truth of the conjecture in one instance, where \(\lambda =\sqrt{-3}\) and the automorphic representation occurs in the cohomology of a congruence subgroup of level 61 in GL(3,\({\mathbb{Z}})\).
scientific article; zbMATH DE number 4173089
scientific article