Hecke eigenvalue of a nonholomorphic Eisenstein series (source code)

= Hecke eigenvalue of a nonholomorphic Eisenstein series

For the normalization $(T_pf)(\tau)=p^{-1}(f(p\tau)+\sum_{b\bmod p}f((\tau+b)/p))$, one has
$$
T_pG(\tau,s)=(p^{s-1}+p^{-s})G(\tau,s).
$$