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.

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