On basis problem for Siegel modular forms of degree 2
نویسندگان
چکیده
منابع مشابه
On the Basis Problem for Siegel-hilbert Modular Forms
In this paper, we mainly announce the result: every Siegel-Hilbert cuspform of weight divisible by 4h and of square-free level relative to certain congruence subgroups is a linear combination of theta series. I N T R O D U C T I O N Theta series provides one of the two most explicit ways to construct holomorphic modular forms. The other way is by Eisenstein series. A virtue of theta series is t...
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In our earlier paper [7], we presented an algorithm for computing explicitly the coset representatives and the action of the Hecke operators on Siegel modular forms for arbitrary degree. The action was expressed in terms of the effect on the lattice-Fourier coefficients of the form (see the introduction for a definition of this term). This expression involved combinatorial terms that count loca...
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The aim of this paper is to give the dimension of the space of Siegel modular forms M k (Γ(3)) of degree 2, level 3 and weight k for each k. Our main result is Theorem dim M k (Γ(3)) = 1 2 (6k 3 − 27k 2 + 79k − 78) k ≥ 4. In other words we have the generating function : ∞ k=0 dim M k (Γ(3))t k = 1 + t + t 2 + 6t 3 + 6t 4 + t 5 + t 6 + t 7 (1 − t) 4. About the space of cusp forms, the dimension ...
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In contrast to this situation, there is currently no satisfactory theory of local newforms for the group GSp(2, F ). As a consequence, there is no analogue of Atkin–Lehner theory for Siegel modular forms of degree 2. In this paper we shall present such a theory for the “square-free” case. In the local context this means that the representations in question are assumed to have nontrivial Iwahori...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1976
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-31-1-17-30