Select the correct newform via traces in CMF GP and Magma code snippets (LMFDB#5403, LMFDB#6060)#28
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Select the correct newform via traces in CMF GP and Magma code snippets (LMFDB#5403, LMFDB#6060)#28roed-math wants to merge 1 commit into
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LMFDB#6060) The GP snippet took f = lf[1] and Magma had no selection, although the GP/Magma eigenbasis order often differs from the LMFDB order (PARI reverses 37.2.a and 34.2.c; Magma reverses 80.5.h from LMFDB#6059). Following the Sage snippet, select the orbit whose absolute eigenvalue traces up to the newspace trace bound match the stored traces: in GP via mfeigenbasis with an abstrace helper (rescaling by field degrees since PARI represents coefficients in subtowers), in Magma via the modular symbols NewformDecomposition, because Newforms(CuspForms(chi,k)) in Magma V2.29-4 silently returns wrong eigenvalues in many character spaces (32.2.g, 110.2.f, 102.2.h). Weight 1 keeps no Magma snippet (Magma has no weight 1 newforms). Adds a snippet_test section so the snippet CI covers newform pages. Verified by running the rendered snippets and full code downloads in gp and Magma for 19 newforms (incl. order-mismatch, nested-coefficient- field, trace_bound 0 and weight 1 cases), comparing traces beyond the selection window with the database; selection costs 0-1 ms in GP and at most ~0.2 s in Magma. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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The Pari/GP snippet on newform pages took
f = lf[1]("index may be different") and Magma had no selection at all, even though the eigenbasis order of GP/Magma often differs from the LMFDB order (e.g. PARI reverses 37.2.a and 34.2.c; Magma reverses 80.5.h from LMFDB#6059). Following the Sage snippet from LMFDB#6515, the GP and Magma snippets now select the newform whose absolute Hecke eigenvalue traces up to the newspace's trace bound match the stored traces. The GP version computes traces frommfeigenbasiswith a smallabstracehelper (rescaling by degrees since PARI represents coefficients in subtowers); the Magma version selects fromNewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(chi,k,-1))))becauseNewforms(CuspForms(chi,k))in current Magma (V2.29-4) silently returns wrong eigenvalues in many character spaces (e.g. 32.2.g, 110.2.f, 102.2.h; verified against LMFDB data, PARI and Magma's own modular symbols). Selection adds 0-1 ms in GP and at most ~0.2 s in Magma on all 19 tested labels, verified by running the generated snippets in both systems and comparing traces beyond the selection window; asnippet_testsection now lets the snippet CI cover newform pages. For weight 1 the Magma snippet is omitted since Magma has no weight-1 newforms (its init already errors there). Addresses LMFDB#5403. Addresses LMFDB#6060.🤖 Generated with Claude Code