  The interplay between strong electron-electron interactions and band topology
can lead to novel electronic states that spontaneously break symmetries. The
discovery of flat bands in magic-angle twisted bilayer graphene (MATBG) with
nontrivial topology has provided a unique platform in which to search for new
symmetry-broken phases. Recent scanning tunneling microscopy and transport
experiments have revealed a sequence of topological insulating phases in MATBG
with Chern numbers $C=\pm 3, \, \pm 2, \, \pm 1$ near moir\'e band filling
factors $\nu = \pm 1, \, \pm 2, \, \pm 3$, corresponding to a simple pattern of
flavor-symmetry-breaking Chern insulators. Here, we report high-resolution
local compressibility measurements of MATBG with a scanning single electron
transistor that reveal a new 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 $C= \pm 1$ 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
moir\'e unit cell and splits each $C=\pm 1$ band into a $C=\pm 1$ band and a
$C=0$ band. Our findings significantly expand the known phase diagram of MATBG,
and shed light onto the origin of the close competition between different
correlated phases in the system.
