Formalized cmf LMFDB definitions - #81
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specifically newforms so the charpoly is known
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IsGaloisConjugate,galoisOrbit,traceForm- though on LMFDB they're defined for only newforms, I kept the definition general for cusp forms.Same with
IsTwist,IsTwistRelated,dual/self-dual,self/inner twists,counts,CM/RM,twistMultiplicity.I think everything else is faithful to the LMFDB side. The general rule is the following: if the construction makes sense to an arbitrary cusp form then we define it for a
cusp form. If the definition genuinely depends on being a newform, we useIsNewform.The Petersson product is now formalized as a genuine integral (mathlib's
peterssonintegrand against its new invariant measure on ℍ, over a caller-supplied fundamental domain), while the definitions depending on it (newspace,eisensteinSubspace,IsNewform) take an abstract pairingBas input, so they can later be specialized to the concrete Petersson product without restating them.(This is outside of my knowledge) but Claude gave me one caveat: the
IsFundamentalDomainhypothesis is unsatisfiable for any group containing −I (e.g. SL(2,ℤ), Γ₀(N)) since −I acts trivially on ℍ — fixing this needs a PSL(2,ℤ)-style reformulation, and making the product non-junk still awaits three mathlib gaps: 𝒟 as a measure-theoretic fundamental domain, finiteness of its volume, and a finite-index coset-transfer lemma.