E. Artin conjectured that the

By combining the main result of a recent paper of K. Buzzard and Taylor with a computer computation, Buzzard and I recently proved that the icosahedral Artin representations of conductor are modular. If I can extend a congruence result of J. Sturm, then our method will yield several more examples. These ongoing computations are laying a part of the foundation necessary for a full proof of the Artin conjecture for odd two-dimensional , as well as stimulating the development of new algorithms for computing with modular forms in characteristic .