  We propose a two-parameter family of modular invariant partition functions of
two-dimensional conformal field theories (CFTs) holographically dual to pure
three-dimensional gravity in anti de Sitter space. Our two parameters control
the central charge, and the representation of $SL(2,\mathbb{Z})$. At large
central charge, the partition function has a gap to the first nontrivial
primary state of $\frac{c}{24}$. As the $SL(2,\mathbb{Z})$ representation
dimension gets large, the partition function exhibits some of the qualitative
features of an irrational CFT. This, for instance, is captured in the behavior
of the spectral form factor. As part of these analyses, we find similar
behavior in the minimal model spectral form factor as $c$ approaches $1$.
