  We study the Mott phases and superfluid-insulator transition of spin-three
bosons in an optical lattice with an anisotropic two dimensional optical trap.
We chart out the phase diagrams for Mott states with $n=1$ and $n=2$ atoms per
lattice site. It is shown that the long-range dipolar interaction stabilizes a
state where the chains of the ferromagnetically aligned spins run along the
longer trap direction while the spin ordering is staggered between nearby
chains, leading to an antiferromagnetic ordering along the shorter trap
direction. We also obtain the mean-field phase boundary for the
superfluid-insulator transition in these systems and study the nature of spin
ordering in the superfluid state near the transition. We show that, inside the
superfluid phase and near the superfluid-insulator phase boundary, the system
undergoes a first order antiferromagnetic-ferromagnetic spin ordering
transition. We discuss implications of our results for $^{52}$Cr atoms and
suggest possible experiments to detect different phases in such systems.
