Comparison of integral structures on spaces of modular forms of weight two, and computation of spaces of forms mod 2 of weight one, with appendices by Jean-Francois Mestre and Gabor Wiese

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dc.creatorEdixhoven, Bas
dc.creatorMestre, Jean-Francois
dc.creatorWiese, Gabor
dc.date2003-12-01
dc.date.accessioned2026-07-07T08:37:48Z
dc.date.available2026-07-07T08:37:48Z
dc.descriptionTwo integral structures on the Q-vector space of modular forms of weight two on X_0(N) are compared at primes p exactly dividing N. When p=2 and N is divisible by a prime that is 3 mod 4, this comparison leads to an algorithm for computing the space of weight one forms mod 2 on X_0(N/2). For p arbitrary and N>4 prime to p, a way to compute the Hecke algebra of mod p modular forms of weight one on Gamma_1(N) is presented, using forms of weight p, and, for p=2, parabolic group cohomology with mod 2 coefficients. Appendix A is a letter from Mestre to Serre, of October 1987, where he reports on computations of weight one forms mod 2 of prime level. Appendix B reports on an implementation for p=2 in Magma, using Stein's modular symbols package, with which Mestre's computations are redone and slightly extended.
dc.description39 pages, Latex
dc.identifierhttps://arxiv.org/abs/math/0312019
dc.identifierhttp://arxiv.org/abs/math/0312019
dc.identifierJ. Inst. Math. Jussieu 5 (2006), no. 1, 1--34.
dc.identifierdoi:10.1017/S1474748005000113
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140532
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject14G35 (Primary) 11F11, 11Y40 (Secondary)
dc.titleComparison of integral structures on spaces of modular forms of weight two, and computation of spaces of forms mod 2 of weight one, with appendices by Jean-Francois Mestre and Gabor Wiese
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