  This is a first part of a series of papers in which we develop explicit
computational methods for automorphic forms for GL(3) and PGL(3) over elliptic
function fields. In this first part, we determine explicit formulas for the
action of the Hecke operators on automorphic forms on GL(2) and GL(3) in terms
of their graphs. Our primary result consists in a complete description of the
graphs of degree 1 Hecke operators for GL(3). As complementary results, we
describe the 'even component' of the graphs of degree 2 Hecke operators for
GL(2) and the 'neighborhood of the identity' of the graphs of degree 2 Hecke
operators for GL(3). In addition, we establish two dualities for Hecke
operators for GL(n) and PGL(n), which hold for all n, all degrees and all
function fields.
