On the Kohnen-Zagier formula in the case of level \(4p^m\)
Let \(g\) be a Hecke eigen newform in Kohnen's space of cusp forms of weight \(k + 1/2\) and level \(4N\), \(N\) squarefree. Let \(f\) be the primitive form of weight \(2k\) associated to \(g\) by the Shimura correspondence. The Kohnen-Zagier formula expresses the Fourier-coefficient \(c_g(|D|)\), \((-1)^kD> 0\), as the product of \(L(f,D,k)\) of the \(L\)-function of \(f\) twisted with \(({D\over.})\) with some elementary factors. In the paper under review the author derives an analogous result for \(N= p^m\), \(p\) odd prime. The main difficulty arises from the fact that Kohnen's space does not necessarily have multiplicity one.
scientific article; zbMATH DE number 2173661