I'm trying to proof the transformation property of the Eisenstein series G(k,X) defined on page 17: https://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/978-3-540-74119-0_1/fulltext.pdf
I already tried to compute the fourier coefficients of the transformed series,but it didn't work. An other idea I had was to use poisson summation formula, but there I can't find a fitting schwartz function. Many thanks in advance!