  We continue the study of random matrix universality in two-dimensional
conformal field theories. This is facilitated by expanding the spectral form
factor in a basis of modular invariant eigenfunctions of the Laplacian on the
fundamental domain. The focus of this paper is on the discrete part of the
spectrum, which consists of the Maass cusp forms. Both their eigenvalues and
Fourier coefficients are sporadic discrete numbers with interesting statistical
properties and relations to analytic number theory; this is referred to as
`arithmetic chaos'. We show that the near-extremal spectral form factor at late
times is only sensitive to a statistical average over these erratic features.
Nevertheless, complete information about their statistical distributions is
encoded in the spectral form factor if all its spin sectors exhibit universal
random matrix eigenvalue repulsion (a `linear ramp'). We `bootstrap' the
spectral correlations between the cusp form basis functions that correspond to
a universal linear ramp and show that they are unique up to theory-dependent
subleading corrections. The statistical treatment of cusp forms provides a
natural avenue to fix the subleading corrections in a minimal way, which we
observe leads to the same correlations as those described by the
[torus]$\times$[interval] wormhole amplitude in AdS${}_3$ gravity.
