Computational aspects of Hilbert modular forms (I, II and III)

Lassina Dembele, Institut für Experimentelle Mathematik

Abstract: These will be a series of three lectures in which the main goal is to show how to work explicitly with Hilbert modular forms using the Hilbert Modular Form Package in Magma. We start with a quick survey of Hilbert modular forms and the Jacquet-Langlands correspondence, followed by a description of the algorithm we use for computing Hecke eigensystems of such objects. The remaining of the course will consist of concrete examples of Hilbert newforms together with the associated geometric objects, i.e. Abelian varieties or Galois repesentations.