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On Higher Congruences Between Cusp Forms and Eisenstein Series

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Computations with Modular Forms

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 6))

Abstract

The paper contains a numerical study of congruences modulo prime powers between newforms and Eisenstein series at prime levels and with equal weights. We study the upper bound on the exponent of the congruence and formulate several observations based on the results of our computations.

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Acknowledgements

The author would like to thank Wojciech Gajda for many helpful suggestions and corrections. He thanks Gerhard Frey for reading an earlier version of the paper and for helpful comments and remarks. He would like to thank Gabor Wiese for his help in improving the paper and suggesting one of the lemmas. Finally, the author wishes to express his thanks to an anonymous referee for the careful reading of the paper and a detailed list of comments which improved the exposition and removed several inaccuracies. The author was supported by the National Science Centre research grant 2012/05/N/ST1/02871.

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Authors and Affiliations

  1. Graduate School, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland

    Bartosz Naskręcki

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  1. Bartosz Naskręcki
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Correspondence to Bartosz Naskręcki .

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Editors and Affiliations

  1. Interdisciplinary Center for Scientific Computing, Universität Heidelberg, Heidelberg, Baden-Württemberg, Germany

    Gebhard Böckle

  2. UR Mathématiques, Faculté des Sciences, de la Technologie et de la Communication, Luxembourg, Luxembourg

    Gabor Wiese

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Naskręcki, B. (2014). On Higher Congruences Between Cusp Forms and Eisenstein Series. In: Böckle, G., Wiese, G. (eds) Computations with Modular Forms. Contributions in Mathematical and Computational Sciences, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-03847-6_10

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