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On some dimension formula for automorphic forms of weight one I

Published online by Cambridge University Press:  22 January 2016

Toyokazu Hiramatsu
Toyokazu Hiramatsu*
Affiliation:
Department of Mathematics, Kobe University
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Let Γ be a fuchsian group of the first kind not containing the element . We shall denote by d0 the number of linearly independent automorphic forms of weight 1 for Γ. It would be interesting to have a certain formula for d0. But, Hejhal said in his Lecture Notes 548, it is impossible to calculate d0 using only the basic algebraic properties of Γ. On the other hand, Serre has given such a formula of d0 recently in a paper delivered at the Durham symposium ([7]). His formula is closely connected with 2-dimensional Galois representations.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 85 , March 1982 , pp. 213 - 221
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

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[ 2 ] Hiramatsu, T., On some dimension formula for automorphic forms of weight one II, to appear.Google Scholar
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[ 7 ] Serre, J.-P., Modular forms of weight one and Galois representations, In: Proc. Symposium on Algebraic Number Fields, 193–268. Academic Press, 1977.Google Scholar