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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   ℓ  ‐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.

Every 7‐Dimensional abelian variety over Q p has a reducible ℓ ‐adic Galois representation