On Artin's Conjecture for Odd 2-dimensional Representations [electronic resource] / by Jacques Basmaji, Ian Kiming, Martin Kinzelbach, Xiangdong Wang, Loïc Merel ; edited by Gerhard Frey.

On the experimental verification of the artin conjecture for 2-dimensional odd galois representations over Q liftings of 2-dimensional projective galois representations over Q -- A table of A5-fields -- A. Geometrical construction of 2-dimensional galois representations of A5-type. B. On the realisation of the groups PSL2(1) as galois groups over number fields by means of l-torsion points of elliptic curves -- Universal Fourier expansions of modular forms -- The hecke operators on the cusp forms of ?0(N) with nebentype -- Examples of 2-dimensional, odd galois representations of A5-type over ? satisfying the Artin conjecture.

The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the dimension of a corresponding space of cusp forms of weight 1 which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols. It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.