Abstract
The cohomology of an arithmetic group is built out of certain automorphic forms. This allows computational investigation of these automorphic forms using topological techniques. We discuss recent techniques developed for the explicit computation of the cohomology of congruence subgroups of GL2 over CM-quartic and complex cubic number fields as Hecke-modules.
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- 1.
For fields whose unit group is rank 0, we do not need reduction Type 0.
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Acknowledgements
This article is based on a lecture delivered by the author at the Computations with Modular Forms 2011 conference at the Universität Heidelberg in September 2011. The author thanks the organizers of the conference Gebhard Böckle (Universität Heidelberg), John Voight (University of Vermont), and Gabor Wiese (Université du Luxembourg) for the opportunity to speak and for being such excellent hosts. Finally, the author thanks the referee for many helpful comments and corrections.
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Yasaki, D. (2014). Computing Modular Forms for GL2 over Certain Number Fields. 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_14
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DOI: https://doi.org/10.1007/978-3-319-03847-6_14
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