The Divisor Matrix, Dirichlet Series and SL(2,Z), II

We examine an elliptic curve constructed in an earlier paper from a certain representation of $\text{SL}(2,\mathbb{Z})$ on the space of convergent Dirichlet series. The curve is observed to be a modular curve for ${\mathrm{\Gamma }}^1(15)$ and a certain orbit of modular functions is thereby associated with the Riemann zeta function. Explicit descriptions are given of these functions and of the permutation action of $\text{SL}(2,\mathbb{Z})$ on them.