Explicit determination of images of Galois representations attached to Hilbert modular forms Original Research Article

In a previous paper the second author proved that the image of the Galois representation modulo λ attached to a Hilbert modular newform is “large” for all but finitely many primes λ, if the newform is not a theta series. In this brief note, we give an explicit bound for this exceptional finite set of primes and determine the images in three different examples. Our examples are of Hilbert newforms on real quadratic fields, of parallel or non-parallel weight and of different levels.