Some vector valued Siegel modular forms of genus 2
نویسندگان
چکیده
is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theorem 2.4), i.e. the dimension formula for the spaces N (r). We prove that M is the intersection of the localizations of N by 60 elements (Theorem 5.4). This is a complete algebraic description of M and to get a finite system of generators of M is a computational problem. At the moment we cannot solve this problem. Examples of elements of M which are not contained in N can be given.
منابع مشابه
Siegel Modular Forms
These are the lecture notes of the lectures on Siegel modular forms at the Nordfjordeid Summer School on Modular Forms and their Applications. We give a survey of Siegel modular forms and explain the joint work with Carel Faber on vector-valued Siegel modular forms of genus 2 and present evidence for a conjecture of Harder on congruences between Siegel modular forms of genus 1 and 2.
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