  We calculate the ground states and ground state phase diagrams of
Bose-Einstein condensates of spin-3 atoms under the assumption of conserved
magnetization. We especially concentrate on the ground states of a chromium
condensate. In chromium the magnetic dipole-dipole interaction enables
magnetization changing collisions, but in a strong magnetic field these are
suppressed. In the calculation of the phase diagrams we neglect the
contribution from the dipole-dipole interaction, but discuss its effects at the
end of the paper. We show that the ground state of a chromium condensate does
not seem to depend on whether or not the dipole-dipole interaction is taken
into attention.
