  We demonstrate the presence of modular properties in partition functions of
$T\bar{T}$ deformed conformal field theories. These properties are verified
explicitly for the deformed free boson. The modular features facilitate a
derivation of the asymptotic density of states in these theories, which turns
out to interpolate between Cardy and Hagedorn behaviours. We also point out a
sub-sector of the spectrum that remains undeformed under the $T\bar{T}$ flow.
Finally, we comment on the deformation of the CFT vacuum character and its
implications for the holographic dual.
