We give generators and relations for the graded rings of Hermitian modular forms of degree two over the rings of integers in \({\mathbb {Q}}(\sqrt{-7})\) and \({\mathbb {Q}}(\sqrt{-11})\). In both cases we prove that the subrings of symmetric modular forms are generated by Maass lifts. The computation uses a reduction process against Borcherds products which also leads to a dimension formula for the spaces of modular forms.

中文翻译：

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厄米模形式的两个分级环

我们给出\({\mathbb {Q}}(\sqrt{-7})\)和\({\mathbb {Q} }(\sqrt{-11})\)。在这两种情况下，我们都证明了对称模形式的子环是由马斯电梯产生的。该计算使用对 Borcherds 产品的归约过程，这也导致了模块化形式空间的维度公式。