  In this article we study the spectrum of totally geodesic surfaces of a
finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic
3-manifolds that contain a totally geodesic surface, this spectrum determines
the commensurability class. In addition, we show that any finite volume
hyperbolic 3-manifold has many pairs of non-isometric finite covers with
identical spectra. Forgetting multiplicities, we can also construct pairs where
the volume ratio is unbounded.
