  We establish the relation of partition functions of conformal higher spin
fields on Weyl equivalent spaces in $d=4$ dimension. We express the partition
function of Weyl graviton and conformal higher spin fields as an integral over
characters on $S^1\times AdS_3$, $S^4$, and $AdS_4$. We observe that the
partition function of conformal higher spins on hyperbolic cylinders differs
from the partition function on $S^4$ by the `edge' contribution. The
logarithmic coefficient obtained from the character integral of the partition
function of conformal higher spins on $AdS_4$ is the half of that obtained from
the partition function on $S^4$. We evaluate the entanglement entropy and the
conformal dimension of the twist operator from the partition function on the
hyperbolic cylinder. The conformal dimension of the co-dimension two twist
operator enables us to find a linear relation between Hofman-Maldacena
variables which we use to show the non-unitarity of the theory. We observe that
the spectrum of the quasinormal modes of conformal higher spins obtained from
the bulk character contains additional distinct states compared to the spectrum
of unitary massless higher spin fields.
