  Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs
algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein
gravity in 3d asymptotically flat spacetimes. When defined on a torus, these
field theories come equipped with a modified modular structure. We use the
modular covariance of the BMS torus two-point function to develop formulae for
different three-point structure constants of the field theory. These structure
constants indicate that BMSFTs follow the eigenstate thermalization hypothesis,
albeit with some interesting changes to usual 2d CFTs. The singularity
structures of the structure constants contain information on perturbations of
cosmological horizons in 3d asymptotically flat spacetimes, which we show can
also be obtained as a limit of BTZ quasinormal modes.
