  Irregular cusp of an orthogonal modular variety is a cusp where the lattice
for Fourier expansion is strictly smaller than the lattice of translation.
Presence of such a cusp affects the study of pluricanonical forms on the
modular variety using modular forms. We study toroidal compactification over an
irregular cusp, and clarify there the cusp form criterion for the calculation
of Kodaira dimension. At the same time, we show that irregular cusps do not
arise frequently: besides the cases when the group is neat or contains -1, we
prove that the stable orthogonal groups of most (but not all) even lattices
have no irregular cusp.
