In this paper we study new invariants $\widehat{ Z}_{ \boldsymbol{ a}}(q)$ attached to plumbed $3$-manifolds that were introduced by Gukov, Pei, Putrov, and Vafa. These remarkable $q$-series at radial limits conjecturally compute WRT invariants of the corresponding plumbed $3$-manifold. Here we investigate the series $\widehat{ Z}_{ 0}(q)$ for unimodular plumbing ${ \tt H}$-graphs with six vertices. We prove that for every positive definite unimodular plumbing matrix, $\widehat{ Z}_{ 0}(q)$ is a depth two quantum modular form on $\mathbb{ Q}$.
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