Nonfreeness of algebras of symmetric Hilbert modular forms of even weight for $\mathbb{Q}(\sqrt{d})$ where d>5

Ekaterina Stuken

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arXiv · 1706.04006

Nonfreeness of algebras of symmetric Hilbert modular forms of even weight for $\mathbb{Q}(\sqrt{d})$ where d>5

Ekaterina Stuken

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Abstract

We study the algebras of symmetric Hilbert modular forms of even weight for $\mathbb{Q}(\sqrt{d})$, considering them as modular forms for the orthogonal group of the lattice with signature (2,2). Comparing the volume of the corresponding symmetric domain with the volume of the Jacobian of the generators of these algebras, we prove that for all d, except for d=2, 3, 5 these algebras can't be free.

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Ekaterina Stuken. 2017-06-13. Nonfreeness of algebras of symmetric Hilbert modular forms of even weight for $\mathbb{Q}(\sqrt{d})$ where d>5. https://arxiv.org/abs/1706.04006

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