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    Roe, David 2014. The 3-adic eigencurve at the boundary of weight space. International Journal of Number Theory, Vol. 10, Issue. 07, p. 1791.


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  • LMS Journal of Computation and Mathematics, Volume 15
  • May 2012, pp. 113-139

Slopes of the U7 operator acting on a space of overconvergent modular forms

  • L. J. P. Kilford (a1) and Ken McMurdy (a2)
  • DOI: http://dx.doi.org/10.1112/S1461157012000095
  • Published online: 01 May 2012
Abstract
Abstract

Let χ be the primitive Dirichlet character of conductor 49 defined by χ(3)=ζ for ζ a primitive 42nd root of unity. We explicitly compute the slopes of the U7 operator acting on the space of overconvergent modular forms on X1(49) with weight k and character χ7k−6 or χ8−7k, depending on the embedding of ℚ(ζ) into ℂ7. By applying results of Coleman and of Cohen and Oesterlé, we are then able to deduce the slopes of U7 acting on all classical Hecke newforms of the same weight and character.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]K. Buzzard , ‘Analytic continuation of overconvergent eigenforms’, J. Amer. Math. Soc. 16 (2003) 2955.

[2]H. Cohen and J. Oesterlé , ‘Dimensions des espaces de formes modulaires’, Modular functions of one variable VI (Bonn, Germany 1976), Lecture Notes in Mathematics 627 (Springer, Berlin, 1977) 6978.

[3]R. Coleman , ‘Classical and overconvergent modular forms’, Invent. Math. 124 (1996) 215241.

[4]R. Coleman , ‘Classical and overconvergent modular forms of higher level’, J. Théor. Nombres Bordeaux 9 (1997) 395403.

[5]R. Coleman , ‘p-adic Banach spaces and families of modular forms’, Invent. Math. 127 (1997) 417479.

[7]P. Deligne and M. Rapoport , ‘Les schémas de modules de courbes elliptiques’, Modular functions of one variable II (Antwerp, Belgium 1972), Lecture Notes in Mathematics 349 (Springer, Berlin, 1973) 143316.

[9]B. Gross , ‘A tameness criterion for Galois representations associated to modular forms (mod p)’, Duke Math. J. 61 (1990) 445517.

[11]L. J. P. Kilford , ‘On the slopes of the U5 operator acting on overconvergent modular forms’, J. Théor. Nombres Bordeaux 20 (2008) 165182.

[13]K. McMurdy , ‘Explicit parametrizations of ordinary and supersingular regions of X0(pn)’, Modular curves and abelian varieties, Progress in Mathematics 224 (Birkhäuser, Basel, 2004) 165179.

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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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