  In the context of warped conformal field theories (WCFT), the derivation of
the warped Cardy formula relies on the zero mode spectrum being bounded from
below. Generically, this is not true for holographic WCFTs in "canonical"
ensemble, whereas this condition is satisfied in the "quadratic" ensemble,
making it more natural in holographic setups. In this work, we find a new set
of boundary conditions in three-dimensional Topologically Massive Gravity (TMG)
such that the putative dual theory is a WCFT in quadratic ensemble.
Surprisingly, imposing the equations of motion, we obtain a closed form metric
spanned by two arbitrary chiral functions, analogous to the Ba\~nados metrics
in Einstein gravity. Surface charges for these boundary conditions are not a
priori integrable and we discuss two choices of boundary conditions to make
them so. We obtain the bulk thermodynamic entropy of warped BTZ black holes by
making use of the warped Cardy formula, in its regime of validity. We also
discuss the issue of identifying the vacuum in our solution space: demanding
the enhancement of global symmetries selects only a family of solutions, out of
which the unique vacuum must be carefully singled out.
