For k≥2 even, let dk,N denote the dimension of the largest simple Hecke submodule of Sk(Γ0(N);Q)new⁠. We show, using a simple analytic method, that dk,N≫kloglogN/log(2p) with p⁠, the smallest prime co-prime to N⁠. Previously, bounds of this quality were only known for N in certain subsets of the primes. We also establish similar (and sometimes stronger) results concerning Sk(Γ0(N),χ)⁠, with k≥2 an integer and χ an arbitrary nebentypus.

A Note on the Dimension of the Largest Simple Hecke Submodule

Bettin, Sandro;
2018-01-01

Abstract

For k≥2 even, let dk,N denote the dimension of the largest simple Hecke submodule of Sk(Γ0(N);Q)new⁠. We show, using a simple analytic method, that dk,N≫kloglogN/log(2p) with p⁠, the smallest prime co-prime to N⁠. Previously, bounds of this quality were only known for N in certain subsets of the primes. We also establish similar (and sometimes stronger) results concerning Sk(Γ0(N),χ)⁠, with k≥2 an integer and χ an arbitrary nebentypus.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1016499
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