  We study a class of newly-introduced CFTs associated with even quadratic
forms of general signature, which we call generalized Narain theories. We first
summarize the properties of these theories. We then consider orbifolds of these
theories, thereby obtaining a large class of non-supersymmetric CFTs with
exactly marginal deformations. We then discuss ensemble averages of such
theories over their moduli space, and obtain a modular form associated with the
quadratic form and an element of the discriminant group. The modular form can
be written as a Poincare series, which contains novel invariants of lens spaces
and suggests the interpretation of the holographic bulk as a theory of anyons.
