  We give an effective version of a result reported by Serre asserting that the
images of the Galois representations attached to an abelian surface with
$\End(A)= \mathbb{Z}$ are as large as possible for almost every prime. Our
algorithm depends on the truth of Serre's conjecture for two dimensional odd
irreducible Galois representations. Assuming this conjecture we determine the
finite set of primes with exceptional image.
