black holes and their host galaxies. Relative to the well-studied and accurately measured local relation [see, e.g., the review of @kormendy_2013], at higher redshifts observations suggest that black holes are more massive compared to their hosts. For example, at $z\simeq1.5$ @Ding2020 find a black hole–stellar mass ratio that is 2.7 times larger than the local relation, while at $z\simeq2$, @peng_2006 find a black hole–bulge mass relation 3–6 times larger. At higher redshifts, existing observations of luminous $z\simeq6$ quasars with ALMA generally find black hole to dynamical mass ratios that are significantly larger than the local relation [e.g. @Maiolino2007; @Riechers2008; @venemans_2012; @Wang2013]. However, many studies claim that high observed relations are a result of selection effects, [@Lauer2007; @Schulze2011; @Schulze2014; @DeGraf2015; @Willott2017; @Ding2020]. ALMA observations of lower-luminosity $z\simeq6$ quasars indeed find these to lie on or below the local relation [@Willott2017; @Izumi2018; @Izumi2019].

To investigate the black hole–stellar mass relation using our HST observations, we convert our host magnitude limits to limits on stellar mass. We calculate UV slopes $\beta$ of the hosts by fitting the relation $m=-2.5\log(\lambda^{\beta+2})+m_0$, equivalent to $f_\lambda\propto\lambda^\beta$, to the two host magnitude limits $m_J$ and $m_H$ at $\lambda=1.25$ and 1.6 $\mu$m respectively. Using this relation and the determined 