  Using special polynomials introduced by Hikami and the second author in their
study of torus knots, we construct classes of $q$-hypergeometric series lying
in the Habiro ring. These give rise to new families of quantum modular forms,
and their Fourier coefficients encode distinguished Maass cusp forms. The
cuspidality of these Maass waveforms is proven by making use of the Habiro ring
representations of the associated quantum modular forms. Thus, we provide an
example of using the $q$-hypergeometric structure of associated series to
establish modularity properties which are otherwise non-obvious. We conclude
the paper with a number of motivating questions and possible connections with
Hecke characters, combinatorics, and still mysterious relations between
$q$-hypergeometric series and {the passage} from positive to negative
coefficients of Maass waveforms.
