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;
2021-01-01
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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
