On Artin’s Conjecture for Odd 2-dimensional Representations

Jacques Basmaji, Ian Kiming, Martin Kinzelbach, Xiangdong Wang, Loïc Merel (auth.), Gerhard Frey (eds.)3540583874, 9783540583875, 0387583874

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.

---

Table of contents :
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….Pages 1-36
A table of A 5 -fields….Pages 37-46
A. Geometrical construction of 2-dimensional galois representations of A 5 -type. B. On the realisation of the groups PSL 2 (1) as galois groups over number fields by means of l-torsion points of elliptic curves….Pages 47-58
Universal Fourier expansions of modular forms….Pages 59-94
The hecke operators on the cusp forms of Γ 0 ( N ) with nebentype….Pages 95-108
Examples of 2-dimensional, odd galois representations of A 5 -type over ℚ satisfying the Artin conjecture….Pages 109-121