Murmurations of weight k=8 newforms for Γ₀(N) in Zubrilina's Theorem

In the plots below, each purple dot at x:=(p/X)^1/2 is the average of m_p(f) := w(p)a_p(f)/p^(k/2-1) taken over all newforms f in S_k(N) and squarefree N in [X,X+Y] with Y=X^1-δ, while the green curve is M_k(x) where M_k is Zubrilina's density function for weight k=8. The green curve will not be visible in frames where it is completely obscured by the purple data dots.

This first plot fixes X=2¹⁷ with δ dynamically increasing from 0.1 to 0.5 in increments of 0.05

Below are individual plots for δ = 0.1, 0.15, 0.2, 0.25, ..., 0.75 and X=2ⁿ with n dynamically from 10 to 17 in each animated plot.

0.1		0.25
0.2		0.25
0.3		0.35
0.4		0.45
0.5		0.55
0.6		0.65
0.7		0.75