Murmurations of weight 4 newforms for Γ₀(N) of squarefree level and dimension 1

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

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