Tsaknias's conjecture on degrees of newform coefficient fields
Fix a weight kkk and, for a level NNN, let dk(N)newd_k(N)^{\mathrm{new}}dk(N)new be the maximum of [Kf:Q][K_f:\mathbb Q][Kf:Q] over newforms f∈Sk(N)f\in\mathcal{S}_k(N)f∈Sk(N), where Kf=Q(af(n):n≥1)K_f=\mathbb Q(a_f(n):n\geq 1)Kf=Q(af(n):n≥1) i…