  The trace anomaly of matter in curved space generates an effective action for
the conformal factor of the metric tensor in $D=4$ dimensions, analogous to the
Polyakov action for $D=2$. We compute the contributions of the
reparameterization ghosts to the central charges for $D=4$, as well as the
quantum contribution of the conformal factor itself. The ghost contribution
satisfies the necessary Wess-Zumino consistency condition only if combined with
the spin-2 modes, whose contributions to the trace anomaly we also discuss.
