On Artin’s Conjecture for Odd 2-dimensional Representations

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The aim of this volume is to develop efficient algorithms by which one can verify Artin’s conjecture for odd two-dimensional representations in a fairly wide range. It describes how to determine the number of all representations with given Artin conductor and determinant, and how 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.