Congruences between cusp forms and linear representations of the Galois group

Let f(z) be a cusp form of type (l,e) on Γ 0 (N) which is a common eigenfunction of all Hecke operators. For such f(z) , Deligne and Serre [1] proved that there exists a linear representation such that the Artin L -function for p is equal to the L -function associated to f(z) .