Using exact diagonalization, we study the projected Hamiltonian with Coulomb interaction in eight flat bands of first magic angle twisted bilayer graphene. Employing U(4) [$\mathrm{U}(4)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(4)$] symmetries nonchiral (chiral) band limit, reduced Hilbert space to an extent that allows for around $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}3,\ifmmode\pm\e...