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.
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