Twisting of Siegel paramodular forms. (English) Zbl 1376.11034
Authors’ abstract: Let \(S_k(\Gamma^{\mathrm{para}}(N))\) be the space of Siegel paramodular forms of level \(N\) and weight \(k\). Fix an odd prime \(p\nmid N\) and let \(\chi\) be a nontrivial quadratic Dirichlet character \(\mod p\). Based on [Int. J. Number Theory 10, No. 4, 1043–1065 (2014; Zbl 1297.11035)], we define a linear twisting map \(\mathcal{T}_\chi:S_k(\Gamma^{\mathrm{para}}(N))\to S_k(\Gamma^{\mathrm{para}}(Np^4))\). We calculate an explicit expression for this twist, give the commutation relations of this map with the Hecke operators and Atkin-Lehner involution for primes \(\ell\neq p\), and prove that the \(L\)-function of the twist has the expected form.
Reviewer: Gabriele Nebe (Aachen)
MSC:
11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
14G35 | Modular and Shimura varieties |
Citations:
Zbl 1297.11035Software:
ecdataReferences:
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