Geodesic
Congruences for Modular Forms mod 2 and Quaternionic S-ideal Classes
Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 1076-1095

Voir la notice de l'article provenant de la source Cambridge University Press

We prove many simultaneous congruences mod 2 for elliptic and Hilbert modular forms among forms with different Atkin–Lehner eigenvalues. The proofs involve the notion of quaternionic $S$ -ideal classes and the distribution of Atkin–Lehner signs among newforms.
DOI : 10.4153/CJM-2017-019-1
Mots-clés : 11F33, 11R52, modular forms, congruences, quaternion algebras 
Martin, Kimball. Congruences for Modular Forms mod 2 and Quaternionic S-ideal Classes. Canadian journal of mathematics, Tome 70 (2018) no. 5, pp. 1076-1095. doi: 10.4153/CJM-2017-019-1
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[1] [1] Deligne, P. amd Serre, J.-P., Formes modulaires de poids 1. Ann. Sci. École Norm. Sup. (4) 7 (1974), 507–530. http://dx.doi.org/10.24033/asens.1277 Google Scholar

[2] [2] Hasegawa, Y. and Hashimoto, K., On type numbers of split orders of definite quaternion algebras. ManuscriptaMath. 88 (1995), no. 4, 525–534. http://dx.doi.Org/10.1007/BF02567839 Google Scholar

[3] [3] Hida, H., Congruence of cusp forms and special values of their zeta functions. Invent. Math. 63 (1981), no. 2, 225–261. http://dx.doi.org/10.1007/BF01393877 Google Scholar

[4] [4] Le Hung, B. V. and Li, C., Level raising mod 2 and arbitrary 2-Selmer ranks. Compos. Math. 152 (2016), no. 8, 1576–1608. http://dx.doi.Org/10.1112/S0010437X16007454 Google Scholar

[5] [5] Martin, K., The Jacquet-Langlands correspondence, Eisenstein congruences, and integral L-values in weight 2. Math. Res. Let., to appear. Google Scholar

[6] [6] Martin, K., Refined dimensions of cusp forms, and equidistribution and bias of signs. arxiv:1 609.05386 Google Scholar

[7] [7] Mazur, B., Modular curves and the Eisenstein ideal. Inst. Hautes Études Sci. Publ. Math. 47 (1977), 33–186. Google Scholar

[8] [8] Pizer, A., The action of the canonical involution on modular forms of weight 2 on Fo(M). Math. Ann. 226 (1977), no. 2, 99–116. http://dx.doi.Org/10.1007/BF01360861 Google Scholar

[9] [9] Shemanske, T. R. and Walling, L. H., Twists of Hilbert modular forms. Trans. Amer. Math. Soc. 338 (1993), no. 1, 375–403, http://dx.doi.org/10.1090/S0002-9947-1993-1102225-X Google Scholar

[10] [10] Yoo, H., Non-optimal levels of a reducible mod I modular representation. arxiv:1409.8342v3 Google Scholar

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