We prove that the graded ring of modular forms of weight divisible by 3 is naturally isomorphic to a certain log canonical ring of the associated elliptic modular surface. This extends the Shioda correspondence between weight 3 cusp forms and holomorphic 2-forms.
"Modular forms of weight $3m$ and elliptic modular surfaces." Proc. Japan Acad. Ser. A Math. Sci. 95 (4) 31 - 36, April 2019. https://doi.org/10.3792/pjaa.95.31