Computations of topological Jacobi forms

We compute, at the prime $2$, the entire descent spectral sequence converging to the homotopy groups of the spectra of topological Jacobi forms ${\mathrm{T}\mathrm{J}\mathrm{F}}_m$ for every index $m\ge 1$. An explicit $\mathrm{T}\mathrm{M}\mathrm{F}$-cellular decomposition ${\mathrm{T}\mathrm{J}\mathrm{F}}_m\simeq \mathrm{T}\mathrm{M}\mathrm{F}\otimes P_m$ reduces the problem to analyzing a finite complex $P_m$ with one even cell in each dimension $\le 2m$ except $2$. We identify all differentials using the cell structure.