  The Bose-Hubbard model subjected to an effective magnetic field hosts a
plethora of phases with different topological orders when tuning the chemical
potential. Using the density matrix renormalization group method, we identify
several gapped phases near the first Mott lobe at strong interactions. They are
connected by a particle-hole symmetry to a variety of quantum Hall states
stabilized at low fillings. We characterize phases of both particle and hole
type and identify signatures compatible with Laughlin, Moore-Read, and Bosonic
Integer Quantum Hall states by calculating the quantized Hall conductance and
by extracting the topological entanglement entropy. Furthermore, we analyze the
entanglement spectrum of a Laughlin state of bosonic particles and holes for a
range of interaction strengths, as well as the entanglement spectrum of a
Moore-Read state. These results further corroborate the existence of
topological states at high fillings, close to the first Mott lobe, as hole
analogues of the respective low-filling states.
