  In this paper we study spin 2 fluctuations around a warped $AdS_3 \times S^2
\times T^4 \times \mathcal{I}_{\rho}$ background in type IIA supergravity with
small $\mathcal{N} = (0,4)$ supersymmetry. We find a class of fluctuations,
which will be called \textit{universal}, that is independent of the background
data and corresponds to operators with scaling dimension $\Delta = 2l +2$,
being $l$ the angular-momentum-quantum-number on the $S^2$ which realises the
$SU(2)_R$ symmetry. We compute the central charge for $\mathcal{N} = (0,4)$
two-dimensional superconformal theories from the action of the spin 2
fluctuations.
