  Let $K$ be a complete, discretely valued field with finite residue field and
$G_K$ its absolute Galois group. The subject of this note is the study of the
set of positive integers $d$ for which there exists an absolutely irreducible
$\ell$-adic representation of $G_K$ of dimension $d$ with rational traces on
inertia. Our main result is that non-Sophie Germain primes are not in this set
when the residue characteristic of $K$ is $> 3$. The result stated in the title
is a special case.
