Abstract
AbstractWe describe a method to compute mod $$\ell $$
ℓ
Galois representations contained in the $${{\text {H}}}_{\acute{\mathrm{e}}\mathrm{t}}^2$$
H
e
´
t
2
of surfaces. We apply this method to the case of a representation with values in $${\text {GL}}_3(\mathbb {F}_9)$$
GL
3
(
F
9
)
attached to an eigenform over a congruence subgroup of $${\text {SL}}_3$$
SL
3
. We obtain, in particular, a polynomial with Galois group isomorphic to the simple group $${\text {PSU}}_3(\mathbb {F}_9)$$
PSU
3
(
F
9
)
and ramified at 2 and 3 only.
Funder
University of Dublin, Trinity College
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Analysis
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