  Let $\pi:\CA\ra S$ be an abelian scheme over a scheme $S$ which is
quasi-projective over an affine noetherian scheme and let $\CL$ be a symmetric,
rigidified, relatively ample line bundle on $\CA$. We show that there is an
isomorphism
  \det(\pi_*\CL)^{\o times 24}\simeq\big(\pi_*\omega_{\CA}^{\vee}\big)^{\o
times 12d}
  of line bundles on $S$, where $d$ is the rank of the (locally free) sheaf
$\pi_*\CL$. We also show that the numbers 24 and $12d$ are sharp in the
following sense: if $N>1$ is a common divisor of 12 and 24, then there are data
as above such that
  \det(\pi_*\CL)^{\o times
(24/N)}\not\simeq\big(\pi_*\omega_{\CA}^{\vee}\big)^{\o times (12d/N)}.
