  We investigate effects of the filled Dirac sea on the $SU(4)$ symmetry
breaking in the integer quantum Hall states of graphene with long-ranged
Coulomb interactions. Our model also includes Hubbard and nearest neighbour
repulsive interactions with strengths $U$ and $V$ respectively. We find that
the symmetry breaking of the $n=0$ Landau levels induces an $SU(4)$
polarization of the Dirac sea. This results in several phases which are absent
when the effects of the Dirac sea are neglected. We compute the phase diagram
in the $U$-$V$ space. We also calculate the excitation gaps in tilted magnetic
fields for all the phases. We compare our model results with experiments and
find a range of $U$ and $V$ that are consistent with them.
