  We obtain new fermionic sum representations for the Virasoro characters of
the confromal field theory describing the ferromagnetic three-state Potts spin
chain. These arise from the fermionic quasi-particle excitations derived from
the Bethe equations for the eigenvalues of the hamiltonian. In the conformal
scaling limit, the Bethe equations provide a description of the spectrum in
terms of one genuine quasi-particle, and two ``ghost'' excitations with a
limited microscopic momentum range. This description is reflected in the
structure of the character formulas, and suggests a connection with the
integrable perturbation of dimensions (2/3,2/3)$^+$ which breaks the $S_3$
symmetry of the conformal field theory down to $Z_2$.
