The interplay between strong electron–electron interactions and band topology can produce electronic states that spontaneously break symmetries. The discovery of flat bands in magic-angle twisted bilayer graphene (MATBG)1,2,3 with non-trivial topology4,5,6,7 has provided a compelling platform in which to search for new symmetry-broken phases. Recent scanning tunnelling microscopy8,9 and transport experiments10,11,12,13 have revealed a sequence of topological insulating phases in MATBG near integer filling of the electronic bands produced by the moiré pattern. These correspond to a simple pattern of flavour-symmetry-breaking Chern insulators that fill bands of different flavours one after the other. Here we report the high-resolution local compressibility measurements of MATBG with a scanning single-electron transistor, which reveal an additional sequence of incompressible states with unexpected Chern numbers observed down to zero magnetic field. We find that the Chern numbers for eight of the observed incompressible states are incompatible with the simple picture in which the bands are sequentially filled. We show that the emergence of these unusual incompressible phases can be understood as a consequence of broken translation symmetry that doubles the moiré unit cell and splits each flavour band in two. Our findings expand the known phase diagram of MATBG, and shed light on the origin of the close competition between different correlated phases in the system.