  We investigate the behavior of vector bundles of conformal blocks for
$sp_{2\ell}$ at level one on $\bar{M}_{0,n}$. We show their first Chern classes
are equivalent to conformal blocks divisors for $sl_2$ at level $\ell$ if and
only if the corresponding vector bundles have rank one or zero, and all become
equal when the Lie algebra $\ell$ is large enough. As a consequence of these
results, we conclude the cone generated by these divisors is polyhedral.
