We use self-consistent Hartree-Fock calculations performed in the full π-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (TBG). We find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system's valley projected C_{2}T symmetry. Broken spin-valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moiré band filling n=±p/4 with integer p=1, 2, 3, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than ∼20, the gapped states do not necessarily break C_{2}T symmetry and as a consequence the insulating states at n=±1/4 and n=±3/4 need not exhibit a quantized anomalous Hall effect.