On the average number of octahedral modular forms

Abstract

λf (p) = Tr(ρ(Frobp)) χ(p) = det(ρ(Frobp)) for all p not dividing N . Following [4], we define SArtin 1/4,k (N,χ) to be the finite set of primitive weight k cupsidal eigenforms which admit an associated Galois representation. If ρ : Gal(Q̄/Q)→ GL2(C) is a Galois representation, we define Pρ to be the composition of ρ with the natural projection GL2(C)→ PGL2… (More)

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