Slopes of modular forms and the Ghost conjecture

We give an algorithm to compute the slope sequence of modular forms with fixed Galois components from its first few entries, which is a refined version of the conjecture of [Buz05]. We use the results of arXiv:2302.07697 on the ghost conjecture from axXiv:1710.01572. These symmetries in slope sequences have potential implication to unexplained symmetries in many Coleman-Mazur eigencurves.

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Journal
ArXiv.org
Published
2025-08-03
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

Slopes of modular forms and the Ghost conjecture

ArXiv.org
Algebraic Geometry and Number Theory
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Slopes of modular forms and the Ghost conjecture

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Abstract

We give an algorithm to compute the slope sequence of modular forms with fixed Galois components from its first few entries, which is a refined version of the conjecture of [Buz05]. We use the results of arXiv:2302.07697 on the ghost conjecture from axXiv:1710.01572. These symmetries in slope sequences have potential implication to unexplained symmetries in many Coleman-Mazur eigencurves.

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Slopes of modular forms and the Ghost conjecture · ArXiv.org (2025) | TGRS Research Map | TGRS