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

Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos