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On the computation of local components of a newform
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Loeffler, David and Weinstein, Jared. (2012) On the computation of local components of a newform. Mathematics of Computation, Vol.81 (No.278). pp. 1179-1200. ISSN 0025-5718
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Official URL: http://dx.doi.org/10.1090/S0025-5718-2011-02530-5
Abstract
The problem. Let f be a cuspidal newform for Γ1(N) with weight k ≥ 2 and character ε. There are well-established methods for computing such forms using modular symbols; see [Ste07]. Let πf be the corresponding automorphic representation of the adèle group GL2(AQ).
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Cusp forms (Mathematics), Adeles |
| Journal or Publication Title: | Mathematics of Computation |
| Publisher: | American Mathematical Society |
| ISSN: | 0025-5718 |
| Date: | 2012 |
| Volume: | Vol.81 |
| Number: | No.278 |
| Page Range: | pp. 1179-1200 |
| Identification Number: | 10.1090/S0025-5718-2011-02530-5 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), National Science Foundation (U.S.) (NSF) |
| Grant number: | EP/F04304X/2 (EPSRC), DMS-0803089 (NSF) |
| References: | [AL78] A. O. L. Atkin andWen Ch’ing Winnie Li, Twists of newforms and pseudo-eigenvalues of W-operators, Invent. Math. 48 (1978), no. 3, 221–243. MR508986 (80a:10040) [BCDT01] Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, On the modularity of elliptic curves over Q: Wild 3-adic exercises, Journal of the Amer. Math. Soc. 14 (2001), 843–939. MR1839918 (2002d:11058) [BCP97] Wieb Bosma, John Cannon, and Catherine Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24(3-4) (1997), 235–265. MR1484478 [BH06] Colin J. Bushnell and Guy Henniart, The local Langlands conjecture for GL(2), Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 335, Springer-Verlag, Berlin, 2006. MR2234120 (2007m:22013) [BM02] Christophe Breuil and Ariane M´ezard, Multiplicit´es modulaires et repr´esentations de GL2(Zp) et de Gal(Qp/Qp) en = p, Duke Math. J. 115 (2002), no. 2, 205–310, With an appendix by Guy Henniart. MR1944572 (2004i:11052) [Bum97] Daniel Bump, Automorphic forms and representations, Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, Cambridge, 1997. MR1431508 (97k:11080) [Car83] Henri Carayol, Sur les repr´esentations -adiques attach´ees aux formes modulaires de Hilbert, C. R. Acad. Sci. Paris. 296 (1983), no. 15, 629–632. MR705677 (85e:11039) [Car86] , Sur les repr´esentations -adiques associ´ees aux formes modulaires de Hilbert, Ann. Sci. ´Ecole Norm. Sup. (4) 19 (1986), no. 3, 409–468. MR870690 (89c:11083) [Cas73a] William Casselman, On some results of Atkin and Lehner, Math. Ann. 201 (1973), 301–314. MR0337789 (49:2558) [Cas73b] , The restriction of a representation of GL2(k) to GL2(o), Math. Ann. 206 (1973), 311–318. MR0338274 (49:3040) [Gel75] Stephen S. Gelbart, Automorphic forms on ad`ele groups, Princeton University Press, Princeton, N.J., 1975, Annals of Mathematics Studies, No. 83. MR0379375 (52:280) [Rio06] Anna Rio, Dyadic exercises for octahedral extensions. II, J. Number Theory 118 (2006), no. 2, 172–188. MR2223979 (2007c:11132) [RT83] J. D. Rogawski and J. B. Tunnell, On Artin L-functions associated to Hilbert modular forms of weight one, Invent. Math. 74 (1983), no. 1, 1–42. MR722724 (85i:11044) [Sag] Sage mathematics software, version 4.4.2, http://www.sagemath.org/. [Ste07] William Stein, Modular forms, a computational approach, Graduate Studies in Mathematics, vol. 79, American Mathematical Society, Providence, RI, 2007, With an appendix by Paul E. Gunnells. MR2289048 (2008d:11037) [Tat79] John Tate, Number theoretic background, Automorphic forms, representations and Lfunctions (Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 3–26. MR546607 (80m:12009) [Wei74] Andr´e Weil, Exercices dyadiques, Invent. Math. 27 (1974), 1–22. MR0379445 (52:350) [Wei09] Jared Weinstein, Hilbert modular forms with prescribed ramification, Int. Math. Res. Not. (2009), no. 8, 1388–1420. MR2496768 (2010f:11070) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/43666 |
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