Axial anomalies in N=4 conformal supergravity

We compute the gravitational U(1) and the non-abelian SU(4) anomalies in pure N=4 conformal supergravity. The former vanishes, the latter does not vanish. However, in coupling the N=4 Yang-Mills matter to N=4 conformal supergravity, the SU(4) axial anomaly vanishes when the gauge group has four generators. The U(1) axial anomaly then no longer vanishes. We conclude that pure N=4 conformal supergravity is inconsistent, whereas the above coupling may be consistent. (orig.)