Koike's Trace Formula
Koike's Trace Formula states that Tr((Uκp)n)=−∑0≤u<√pn (u,p)=1H(u2−4pn)γ(u)κγ(u)2−pn−1, where κ∈Cp, H(D) is the Hurwitz class number of D, and γ(u) is the unique p-adic unit root of the equation x2−ux+pn=0. Is there an implementation of this formula in sage ?
Please help us with the initialization of the involved objects, by sharing with us already existing code - even if it does not work properly. Some choice of the many involved symbols p,u,n,κ that may be of interest - with the expected values for the results - would be a great help also. Both sides should be implemented? What is Uκp if yes? Some self-contained reference for the framework would be also useful for a potential answerer.