$2$-adic slopes of Hilbert modular forms over $\mathbb{Q}(\sqrt{5})$

Christopher Birkbeck

doi:10.1112/blms.12361

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arXiv · 1811.04799

$2$-adic slopes of Hilbert modular forms over $\mathbb{Q}(\sqrt{5})$

Christopher Birkbeck

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Abstract

We show that for arithmetic weights with a fixed finite order character, the slopes of $U_p$ (for $p=2$) acting on overconvergent Hilbert modular forms of level $U_0(4)$ are independent of the (algebraic part of the) weight and can be obtained by a simple recipe from the classical slopes in parallel weight $3$.

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BibTeX RIS

Christopher Birkbeck. 2018-11-12. $2$-adic slopes of Hilbert modular forms over $\mathbb{Q}(\sqrt{5})$. https://doi.org/10.1112/blms.12361

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