Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

On the computation of local components of a newform


Authors: David Loeffler and Jared Weinstein
Journal: Math. Comp. 81 (2012), 1179-1200
MSC (2010): Primary 11F70; Secondary 11F11, 11Y99
DOI: https://doi.org/10.1090/S0025-5718-2011-02530-5
Published electronically: September 20, 2011
Erratum: Math. Comp. 84 (2015), 355-356
MathSciNet review: 2869056
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [AL78] A. O. L. Atkin and Wen Ch'ing Winnie Li, Twists of newforms and pseudo-eigenvalues of $ W$-operators, Invent. Math. 48 (1978), no. 3, 221-243. MR 508986 (80a:10040)
  • [BCDT01] Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, On the modularity of elliptic curves over $ \mathbf{Q}$: Wild 3-adic exercises, Journal of the Amer. Math. Soc. 14 (2001), 843-939. MR 1839918 (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. MR 1484478
  • [BH06] Colin J. Bushnell and Guy Henniart, The local Langlands conjecture for $ \operatorname{GL}(2)$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 335, Springer-Verlag, Berlin, 2006. MR 2234120 (2007m:22013)
  • [BM02] Christophe Breuil and Ariane Mézard, Multiplicités modulaires et représentations de $ \operatorname{GL}_2(\mathbf{Z}_p)$ et de $ \operatorname{Gal}(\overline{\mathbf{Q}}_p/\mathbf{Q}_p)$ en $ \ell=p$, Duke Math. J. 115 (2002), no. 2, 205-310, With an appendix by Guy Henniart. MR 1944572 (2004i:11052)
  • [Bum97] Daniel Bump, Automorphic forms and representations, Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, Cambridge, 1997. MR 1431508 (97k:11080)
  • [Car83] Henri Carayol, Sur les représentations $ \ell$-adiques attachées aux formes modulaires de Hilbert, C. R. Acad. Sci. Paris. 296 (1983), no. 15, 629-632. MR 705677 (85e:11039)
  • [Car86] -, Sur les représentations $ \ell$-adiques associées aux formes modulaires de Hilbert, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 3, 409-468. MR 870690 (89c:11083)
  • [Cas73a] William Casselman, On some results of Atkin and Lehner, Math. Ann. 201 (1973), 301-314. MR 0337789 (49:2558)
  • [Cas73b] -, The restriction of a representation of $ \operatorname{GL}_2(k)$ to $ \operatorname{GL}_2({\mathfrak{o}})$, Math. Ann. 206 (1973), 311-318. MR 0338274 (49:3040)
  • [Gel75] Stephen S. Gelbart, Automorphic forms on adèle groups, Princeton University Press, Princeton, N.J., 1975, Annals of Mathematics Studies, No. 83. MR 0379375 (52:280)
  • [Rio06] Anna Rio, Dyadic exercises for octahedral extensions. II, J. Number Theory 118 (2006), no. 2, 172-188. MR 2223979 (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. MR 722724 (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. MR 2289048 (2008d:11037)
  • [Tat79] John Tate, Number theoretic background, Automorphic forms, representations and $ L$-functions (Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 3-26. MR 546607 (80m:12009)
  • [Wei74] André Weil, Exercices dyadiques, Invent. Math. 27 (1974), 1-22. MR 0379445 (52:350)
  • [Wei09] Jared Weinstein, Hilbert modular forms with prescribed ramification, Int. Math. Res. Not. (2009), no. 8, 1388-1420. MR 2496768 (2010f:11070)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11F70, 11F11, 11Y99

Retrieve articles in all journals with MSC (2010): 11F70, 11F11, 11Y99


Additional Information

David Loeffler
Affiliation: Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: d.a.loeffler@warwick.ac.uk

Jared Weinstein
Affiliation: Department of Mathematics, UCLA, Los Angeles, California 90095-1555
Email: jared@math.ucla.edu

DOI: https://doi.org/10.1090/S0025-5718-2011-02530-5
Received by editor(s): August 16, 2010
Received by editor(s) in revised form: February 3, 2011
Published electronically: September 20, 2011
Additional Notes: The first author’s research is supported by EPSRC Postdoctoral Fellowship EP/F04304X/2
The second author’s research is supported by NSF Postdoctoral Fellowship DMS-0803089
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society