  We consider KdV currents in a quantum field theory obtained by deforming a
two dimensional conformal field theory on a cylinder via the irrelevant
operator $T{\bar T}$. In this paper we determine their one-point functions
modular properties. We find that the one-point functions factorize into two
components each with a definite modular weight. We also obtain a general
differential equation that the generalized torus partition sum satisfies.
