The twisted bilayer graphene (TBG) near the first magic angle hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at various integer fillings. In this talk we will discuss the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band and chiral limits. These enlarged symmetries allow us to identify exact or approximate ground or low-energy (Chern) insulator states at all the integer filling factors under a weak assumption that we justify numerically. We can also have access to exact charge and neutral excitations. Finally, we will discuss how scanning tunneling microscopy might be able to discriminate between the different insulating phases proposed in the literature.