Explicit computation of a Galois representation attached to an eigenform over SL3 from the H2 \'etale of a surface

Abstract

We sketch a method to compute mod $\ell$ Galois representations contained in the H2 \'etale of surfaces. We apply this method to the case of a representation with values in GL(3,9) 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(3,9) and ramified at 2 and 3 only.