The Library
On ℓadic representations for a space of noncongruence cuspforms
Tools
Hoffman, Jerome William, Long, Ling and Verrill, Helena. (2012) On ℓadic representations for a space of noncongruence cuspforms. Proceedings of the American Mathematical Society, Vol.140 (No.5). pp. 15691584. ISSN 00029939

Text
WRAP_Verrill_On_adic_representations.pdf  Published Version Download (293Kb)  Preview 


Text (Coversheet)
WRAP_Verrill_On_adic_representations_coversheet.pdf  Supplemental Material Download (49Kb)  Preview 
Official URL: http://dx.doi.org/10.1090/S000299392011110451
Abstract
This paper is concerned with a compatible family of 4dimensional ℓadic representations ρℓ of GQ := Gal(Q/Q) attached to the space of weight3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that:
1.
It is automorphic: the Lfunction L(s,ρℓ∨) agrees with the Lfunction for an automorphic form for GL4(AQ), where ρℓ∨ is the dual of ρℓ.
2.
For each prime p≥5 there is a basis hp = {hp+, hp} of S3(Γ) whose expansion coefficients satisfy 3term Atkin and SwinnertonDyer (ASD) relations, relative to the qexpansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12.
The key point is that the representation ρℓ admits a quaternion multiplication structure in the sense of Atkin, Li, Liu, and Long.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Cusp forms (Mathematics) 
Journal or Publication Title:  Proceedings of the American Mathematical Society 
Publisher:  American Mathematical Society 
ISSN:  00029939 
Official Date:  May 2012 
Volume:  Vol.140 
Number:  No.5 
Page Range:  pp. 15691584 
Identification Number:  10.1090/S000299392011110451 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Open Access 
Funder:  United States. National Security Agency (USNSA), National Science Foundation (U.S.) (NSF), Louisiana Board of Regents 
Grant number:  H982300810076 (NSA), DMS0353722 (NSF), LEQSF (20022004)ENHTR17 (LBR), LEQSF (20042007)RDA16 (LBR), DMS0501318 (NSF) 
References:  [ALLL10] A. O. L. Atkin, W. C. Li, T. Liu, and L. Long, Galois representations with quaternion 
URI:  http://wrap.warwick.ac.uk/id/eprint/48230 
Request changes or add full text files to a record
Actions (login required)
View Item 
Downloads
Downloads per month over past year