  Up to the third post-Newtonian (3PN) order, we compute (i) the current-type
quadrupole moment of (non-spinning) compact binary systems, as well as (ii) the
corresponding gravitational-wave mode $(2,1)$ (constituting a 3.5PN correction
in the waveform). Moreover, at this occasion, (iii) we recompute and confirm
the previous calculation of the mass-type octupole moment to 3PN order. The
ultra-violet (UV) divergences due to the point-like nature of the source are
treated by means of dimensional regularization. This entails generalizing the
definition of the irreducible mass and current multipole moments of an isolated
PN source in $d$ spatial dimensions. In particular, we find that the current
type moment has the symmetry of a particular mixed Young tableau and that, in
addition, there appears a third type of moment which is however inexistent in 3
spatial dimensions.
