  For a pseudodifferential operator $S$ of order 0 acting on sections of a
vector bundle $B$ on a compact manifold $M$ without boundary, we associate a
differential form of order dimension of $M$ acting on $C^\infty(M)\times
C^\infty(M)$. This differential form $\Omega_{n,S}$ is given in terms of the
Wodzicki 1-density $\wres([S,f][S,h])$. In the particular case of an even
dimensional, compact, conformal manifold without boundary, we study this
differential form for the case $(B,S)=(\cH,F)$, that is, the Fredholm module
associated by A. Connes to the manifold $M.$ We give its explicit expression in
the flat case and then we address the general case.
