  In this manuscript, we derive symmetry indicator formulas for the filling
anomaly on 2D square lattices with and without time reversal, inversion
symmetry, or their product, in the presence of spin-orbit coupling. We go
beyond previous work by considering lattices with atoms occupying multiple
Wyckoff positions. We also provide an algorithm using the Smith normal form
that systematizes the derivation. The formulas determine the corner charge in
2D atomic or fragile topological insulators, as well as in 3D insulators and
semimetals by studying their 2D slices. We apply our results to a 3D
tight-binding model on a body-centered tetragonal lattice, whose projection
into the 2D plane has two atoms in the unit cell. Our symmetry indicators
correctly describe the higher-order hinge states and Fermi arcs in cases where
the existing indicators do not apply.
