I will describe a non-perturbative definition of RMT2: a generalization of random matrix theory that is compatible with the symmetries of 2d CFT. Given any random matrix ensemble, its spectral correlations admit a modular-invariant lift to RMT2, which reduce to the original random matrix correlators in a near-extremal limit. The lift proceeds in two steps: I will first discuss a Mellin space formulation of RMT. The Mellin space correlators are then interpreted as an SL(2,Z) spectral decomposition. This sheds a new light on the AdS3 wormhole geometries with multiple torus boundaries.