Murmurations of weight 12 newforms for Γ₀(N)

Each blue/red dot at (p,a_p) records the average of a_p(f)/p⁵ over newforms of root number w(f)=+1/-1 with level in a varying dyadic interval.

Each purple dot at (p,a_p) records the average of w(f)a_p(f)/p⁵ over newforms with level in a varying dyadic interval.