  On a 6-dimensional, conformal, oriented, compact manifold $M$ without
boundary, we compute a whole family of differential forms $\Omega_6(f,h)$ of
order 6, with $f,h \in C^\infty(M).$ Each of these forms will be symmetric on
$f,$ and $h,$ conformally invariant, and such that $\int_M f_0
\Omega_6(f_1,f_2)$ defines a Hochschild 2-cocycle over the algebra
$C^\infty(M).$ In the particular 6-dimensional conformally flat case, we
compute the unique one satisfying $\Wres(f_0[F,f][F,h]) = \int_M
f_0\Omega_6(f,h)$ for $(\cH,F)$ the Fredholm module associated by A. Connes
\cite{Con1} to the manifold $M,$ and $\Wres$ the Wodzicki residue.
