  We study the importance of spin structures as defining data for 11d
supergravity backgrounds of the form AdS$_4\times S^7/\mathbf{Z}_k$ with a free
orbifold action. For a generic choice of the orbifold action, there is only one
spin structure that preserves invariant Killing spinors. There are, however,
orbifold actions that allow for more than one spin structure with preserved
Killing spinors. In these cases the two different spin structures should lead
to distinct holographically dual 3d SCFTs with different amounts of
supersymmetry. We illustrate this phenomenon by studying the KK spectrum of 11d
supergravity on AdS$_4\times S^7/\mathbf{Z}_4$. For one choice of spin
structure this background is dual to the 3d $\mathcal{N}=6$ ABJM theory at
level $k=4$. For the alternative choice of spin structure our results suggest
that the holographic dual is a different 3d $\mathcal{N}=2$ SCFT and we discuss
some of its properties.
