Harris--Venkatesh conjecture for derived Hecke operators on weight-1 forms
Harris--Venkatesh conjecture. There are an element u∈U(Ad(ρ))u\in\mathcal{U}(\operatorname{Ad}(\rho))u∈U(Ad(ρ)) and a positive integer mmm such that, for any primes p,ℓ≥5p,\ell\geq 5p,ℓ≥5 coprime to NNN,