Explicit determination of images of Galois representations attached to Hilbert modular forms

Details Explicit determination of images of Galois representations attached to Hilbert modular forms Explicit determination of images of Galois representations attached to Hilbert modular forms

2004-06-23

arxiv.org/abs/math/0406461v2

Mathematics

Number Theory

7 pages, improved and expanded version

Scientific paper

In a previous article, the second author proved that the image of the Galois representation mod $\lambda$ attached to a Hilbert modular newform is large or all but finitely many primes $\lambda$, if the form 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.

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