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We present the first systematic study of the filling constraints to realize a`trivial' insulator symmetric under magnetic space group $\mathcal{M}$. Thefilling $\nu$ must be an integer multiple of $m^{\mathcal{M}}$ to avoidspontaneous symmetry breaking or fractionalization in gapped phases. We improvethe value of $m^{\mathcal{M}}$ in the literature and prove the tightness of theconstraint for the majority of magnetic space groups. The result may shed lighton the material search of exotic magnets with fractionalization.

The Lieb-Schultz-Mattis-type filling constraints in the 1651 magnetic space groups