Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

We identify states favored by Coulomb interactions projected onto the Wannier basis of the four narrow bands of the ``magic angle'' twisted bilayer graphene. At the filling of 2 electrons/holes per moir\'e unit cell, such interactions favor an insulating $SU(4)$ ferromagnet. The kinetic terms select the ground state in which the two valleys with opposite spins are equally mixed, with a vanishing magnetic moment per particle. We also find extended excited states, the gap to which decreases in the magnetic field. An insulating stripe ferromagnetic phase is favored at 1 electron/hole per unit cell.