A mod five approach to modularity of icosahedral Galois representations

Kevin Buzzard and William A. Stein

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 also 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.