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On ℓadic representations for a space of noncongruence cuspforms
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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

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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  
Dates: 


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 
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