  In this article we investigate the action of (ramified and unramified) Hecke
operators on automorphic forms for the function field of the projective line
defined over a finite field and for the group GL_2. We first compute the
dimension of the Hecke eigenspaces for every generator of the unramified Hecke
algebra. Thus, we consider the ramification in a point of degree one and
describe explicitly the action of certain ramified Hecke operators on
automorphic forms. Moreover, for those ramified Hecke operators, we also
compute the dimensions of its eigenspaces. We finish the article considering
more general ramifications, namely, those one attached to a closed point of
higher degree.
