  We consider mixed branches of 3d $\mathcal{N}=4$ $T[SU(N)]$ theory. We
compute the Hilbert series of the Coulomb branch part of the mixed branch from
a restriction rule acting on the Hilbert series of the full Coulomb branch that
will truncate the magnetic charge summation only to the subset of BPS dressed
monopole operators that arise in the Coulomb branch sublocus where the mixed
branch stems. This restriction can be understood directly from the type IIB
brane picture by a relation between the magnetic charges of the monopoles and
brane position moduli. We also apply the restriction rule to the Higgs branch
part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show
complete agreement with the results calculated by different methods.
