  In this work we consider constructions of genus three curves $X$ such that
$\mathrm{End}(\mathrm{Jac} (X))\otimes Q$ contains the totally real cubic
number field $Q(\zeta _7 +\bar{\zeta}_7 )$. We construct explicit
three-dimensional families whose generic member is a nonhyperelliptic genus 3
curve with this property. The case when $X$ is hyperelliptic was studied in a
previous work by Hoffman and Wang and some nonhyperelliptic curves were
constructed in a previous paper by Hoffman, Z. Liang. Sakai and Wang.
