On the modularity of the unified WRT invariants of certain Seifert manifolds

We compute the unified WRT invariants of the Seifert manifolds M(2,3,8) and M(2,3,4) (arising from ±2 surgery on the trefoil knot). The first is essentially a mock theta function which is a piece of one of Ramanujanʼs third order mock theta functions. The second is essentially the sum of a modular form and a false theta function.