  We discuss ensemble averages of two-dimensional conformal field theories
associated with an arbitrary indefinite lattice with integral quadratic form
$Q$. We provide evidence that the holographic dual after the ensemble average
is the three-dimensional Abelian Chern-Simons theory with kinetic term
determined by $Q$. The resulting partition function can be written as a modular
form, expressed as a sum over the partition functions of Chern-Simons theories
on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons
theory, and we identify several novel phenomena in this case. We also discuss
the holographic duality prior to averaging in terms of Maxwell-Chern-Simons
theories.
