  Following recent developments in the classification of bosonic short-range
entangled phases, we examine many-body quantum systems whose ground state
fractionalization obeys the Lieb-Schultz-Mattis (LSM) theorem. We generalize
the topological classification of such phases by LSM anomalies
(arXiv:1907.08204) to take magnetic and non-symmorphic lattice effects into
account, and provide direct computations of the LSM anomaly in specific
examples. We show that the anomaly-free condition coincides with established
filling constraints (arXiv:1705.09298, arXiv:1505.04193), and we also derived
new ones on novel crystalline quantum systems.
