Abstract
We show that the ring of modular forms with characters for $\mathrm{O}(2,4;\mathbb{Z})$ is generated by forms of weights 4, 4, 6, 8, 10, 10, 12, and 30 with three relations of weights 8, 20, and 60. The proof is based on the study of a moduli space of K3 surfaces.
Acknowledgment
We thank Kenji Hashimoto for valuable discussions, and the anonymous referee for suggestions for improvement. A. N. was partially supported by JSPS Kakenhi (18K13383, MEXT LEADER). K. U. was partially supported by JSPS Kakenhi (15KT0105, 16K13743, 16H03930).
Citation
Atsuhira NAGANO. Kazushi UEDA. "The ring of modular forms of $\mathrm{O}(2,4;\mathbb{Z})$ with characters." Hokkaido Math. J. 51 (2) 275 - 286, June 2022. https://doi.org/10.14492/hokmj/2020-355
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