Moduli Spaces of Shtukas over the Projective Line

We provide explicit equations for moduli spaces of Drinfeld shtukas over the projective line with $\mathrm{\Gamma }(N)$, ${\mathrm{\Gamma }}_1(N)$ and ${\mathrm{\Gamma }}_0(N)$ level structures, where $N$ is an effective divisor on ${\mathbb{P}}^1$. If the degree of $N$ is high enough, these moduli spaces are relative surfaces. We study some invariants of the moduli space of shtukas with ${\mathrm{\Gamma }}_0(N)$ level structure for several degree $4$ divisors on ${\mathbb{P}}^1$.