  Artin conjectured that certain Galois representations should give rise to
entire L-series. We give some history on the conjecture and motivation of why
it should be true by discussing the one-dimensional case. The first known
example to verify the conjecture in the icosahedral case did not surface until
Buhler's work in 1977. We explain how this icosahedral representation is
attached to a modular elliptic curve isogenous to its Galois conjugates, and
then explain how it is associated to a cusp form of weight 5 with level prime
to 5.
