  We give combinatorial models for complex, smooth, non-spherical, generic,
irreducible representations of the group G=PGL(2,F), where F is a
non-archimedean locally compact field. They use the graphs X_k lying above the
tree of G, introduced in a previous work. We show that such representations may
be realized as quotients of the cohomology of X_k for some k, or equivalently
as spaces of discrete harmonic forms on X_k. For supercuspidal representations
these models are unique.
