Supersymmetric spectroscopy on AdS4 × S7 and AdS4 × S6

New techniques based on Exceptional Field Theory have recently allowed for the calculation of Kaluza-Klein spectra certain AdS$_4$ solutions $D=11$ and massive IIA supergravity. These are that consistently uplift $S^7$ $S^6$ from vacua maximal four-dimensional supergravity with SO(8) ISO(7) gaugings. In this paper, we provide complete spectrum five such solutions, all them ${\cal N}=1$. preserve SO(3) $\textrm{U}(1) \times \textrm{U}(1)$ internal symmetry in $D=11$, U(1) (two them) no continuous type IIA. Together previously discussed cases, our results exhaust known supersymmetric relevant class.