  We derive a formula for the torus partition sum of the symmetric product of
$T\bar T$ deformed CFT's, using previous work on long strings in (deformed)
$AdS_3$, and universality. The result is given by an integral transform of the
partition function for the block of the symmetric product, summed over its
Hecke transforms, and is manifestly modular invariant. The spectrum is
interpretable as a gas of multiply wound long strings with a particular
orientation.

High Energy Physics - Theory