  Let $S$ be an oriented, closed surface of genus $g.$ The mapping class group
of $S$ is the group of orientation preserving homeomorphisms of $S$ modulo
isotopy. In 1997, Looijenga introduced the Prym representations, which are
virtual representations of the mapping class group that depend on a finite,
abelian group. Let $V$ be a genus $g$ handlebody with boundary $S$. The
handlebody group is the subgroup of those mapping classes of $S$ that extend
over $V.$ The twist group is the subgroup of the handlebody group generated by
twists about meridians. Here, we restrict the Prym representations to the
handlebody group and further to the twist group. We determine the image of the
representations in the cyclic case.
