  We study the spectrum, unitarity bound and holographic central charge of
spin-2 operators in a warped $\text{AdS}_2 \times \text{S}^2 \times \text{T}^4
\times \mathcal{I}_\psi \times \mathcal{I}_\rho$ background in the Type IIB
theory. We were able to identify a class of solutions that is completely
independent of the functions that define the background solution. We comment on
the relation of our results to the previous ones in the literature.
