Vol. 203, No. 2, 2002

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A mod five approach to modularity of icosahedral Galois representations

Kevin Buzzard and William A. Stein

Vol. 203 (2002), No. 2, 265–282
Abstract

We give eight new examples of icosahedral Galois representations that satisfy Artin’s conjecture on holomorphicity of their L-function. We give in detail one example of an icosahedral representation of conductor 1376 = 25 43 that satisfies Artin’s conjecture. We briefly explain the computations behind seven additional examples of conductors 2416 = 24 151, 3184 = 24 199, 3556 = 22 7 127, 3756 = 22 3 313, 4108 = 22 13 79, 4288 = 26 67, and 5373 = 33 199. We also generalize a result of Sturm on computing congruences between eigenforms.

Milestones
Received: 28 June 2000
Revised: 18 October 2000
Published: 1 April 2002
Authors
Kevin Buzzard
Department of Mathematics
Imperial College
180 Queen’s Gate
London, SW7 2BZ, England
William A. Stein
Department of Mathematics
Harvard University
Cambridge, MA 02138