TY - JOUR
T1 - A Note on the Dimension of the Largest Simple Hecke Submodule
AU - Bettin, Sandro
AU - Perret-Gentil, Corentin
AU - Radziwiłł, Maksym
N1 - Publisher Copyright:
© 2018 The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].
PY - 2021/4/1
Y1 - 2021/4/1
N2 - For k 2 even, let dk,N denote the dimension of the largest simple Hecke submodule of Sk(0(N);Q)new. We show, using a simple analytic method, that dk,N k log logN/ 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(0(N), ), with k 2 an integer and an arbitrary nebentypus.
AB - For k 2 even, let dk,N denote the dimension of the largest simple Hecke submodule of Sk(0(N);Q)new. We show, using a simple analytic method, that dk,N k log logN/ 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(0(N), ), with k 2 an integer and an arbitrary nebentypus.
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U2 - 10.1093/imrn/rny287
DO - 10.1093/imrn/rny287
M3 - Article
AN - SCOPUS:85122210008
SN - 1073-7928
VL - 2021
SP - 4907
EP - 4919
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 7
ER -