  The close relationship between the scheme of level structures on the
universal deformation of a formal group and the Morava $E$-cohomology of finite
abelian groups has played an important role in the study of power operations
for Morava $E$-theory. The goal of this paper is to explore the relationship
between level structures on the $p$-divisible group given by the trivial
extension of the universal deformation by a constant $p$-divisible group and
the Morava $E$-cohomology of the iterated free loop space of the classifying
space of a finite abelian group.
