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A newform theory for mod-p Katz modular forms

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Abstract

In this paper, we provide a definition of mod-p Katz newforms. Then strong multiplicity-one theorems for mod-p Katz modular forms are proved. We show that a cuspidal mod-p Katz eigenform which admits an irreducible Galois representation is in the level- and weight-old space of a uniquely associated mod-p Katz newform. We also set up variants of multiplicity-one results for mod-p Katz eigenforms which have reducible Galois representation.

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Acknowledgements

The author would like to thank his advisor Gabor Wiese for his valuable discussions, remarks and comments which improve the quality of the paper which is the product of the dissertation, and Ian Kiming and Samuele Anni for their comments on the manuscript. I would like to thank Lassina Dembele for his help using Magma. I would also like to thank the referee for the comments including to pointing out that the proof we give for Theorem 1.2 did not work for \(p=2\).

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  1. Department of Mathematics, Addis Ababa University, 1176, Addis Ababa, Ethiopia

    Daniel Mamo

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Correspondence to Daniel Mamo.

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Daniel Mamo is supported by the Luxembourg National Research Fund PRIDE 15/10949314/GSM.

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Mamo, D. A newform theory for mod-p Katz modular forms. Ramanujan J 60, 861–884 (2023). https://doi.org/10.1007/s11139-022-00651-8

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