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On type numbers of split orders of definite quaternion algebras

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Abstract

In this paper, we shall give a new relation between the arithmetic of quaternion algebras and modular forms; we shall express the type numberT q, N of a split order of type (q, N) as the sums of dimensions of some subspaces of the space of cusp forms of weight 2 with respect to Γ0(qN) which are common eigenspaces of Atkin-Lehner's involutions.

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Authors and Affiliations

  1. Department of Mathematics, Waseda University, 3-4-1, Okubo Shinjuku-ku, 169, Tokyo, Japan

    Yuji Hasegawa & Ki-ichiro Hashimoto

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  1. Yuji Hasegawa
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  2. Ki-ichiro Hashimoto
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Hasegawa, Y., Hashimoto, Ki. On type numbers of split orders of definite quaternion algebras. Manuscripta Math 88, 525–534 (1995). https://doi.org/10.1007/BF02567839

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  • DOI: https://doi.org/10.1007/BF02567839

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