Lefschetz coefficients of quantum theta functions

We prove that the coefficients of quantum theta functions in the skew-symmetric setting are characters of finite-dimensional $\mathfrak{sl}_2$ representations. This proves Conjectures 1.4, 2.17 and 3.13 of Davison–Mandel and the two-wall conjecture stated as Conjecture 3.12 in Davison’s ICM 2026 survey.