Some explicit elliptic modular surfaces

We consider algebraic surfaces, recently constructed by Schreieder, that are smooth models of the quotient of the self-product of a complex hyperelliptic curve by a $(\mathbb{Z}\mathrm{/}{3}^c\mathbb{Z})$-action. We show that these surfaces are elliptic modular surfaces in the sense of Shioda, meaning in particular that they are universal families of explicit moduli of elliptic curves.