  We examine trends in the wavevectors and form-factors of charge density wave
instabilities of three-band models of the underdoped cuprates. For
instabilities from a high temperature state with a large Fermi surface, we
extend a study by Bulut et al. (arXiv:1305.3301) to include a direct
antiferromagnetic exchange coupling between the Cu sites. As in previous work,
we invariably find that the primary instability has a diagonal wavevector $(\pm
Q_0, \pm Q_0)$ and a $d$-form factor. The experimentally observed wavevectors
along the principal axes $(\pm Q_0,0)$, $(0, \pm Q_0)$ have higher energy, but
they also have a predominantly $d$-form factor. Next, we gap out the Fermi
surface in the anti-nodal regions of the Brillouin zone by including static,
long-range antiferromagnetic order at the wavevector $(\pi, \pi)$: this is a
simple model of the pseudogap in which we assume the antiferromagnetic order
averages to zero by `renormalized classical' thermal fluctuations in its
orientation, valid when the antiferromagnetic correlation length is large. The
charge density wave instabilities of this pseudogap state are found to have the
optimal wavevector $(\pm Q_0,0)$, $(0, \pm Q_0)$, with the magnitude of the
$d$-form factor decreasing with increasing magnetic order.
