Explicit Computation of a Galois Representation Attached to an Eigenform Over SL 3 from the He´t2 of a Surface

Abstract

We describe a method to compute mod ℓ Galois representations contained in the He´t2 of surfaces. We apply this method to the case of a representation with values in GL 3(F9) attached to an eigenform over a congruence subgroup of SL 3. We obtain, in particular, a polynomial with Galois group isomorphic to the simple group PSU 3(F9) and ramified at 2 and 3 only. © 2022, The Author(s).