On dimension formulas for Jacobi forms (Q848836)

The authors consider Jacobi forms of integral weight \(k\) and index \(S\) being a positive definite half-integral \(l\times l\) matrix, which are defined on \(\mathcal{H}_n\times \mathbb{C}^{\; l\times n}\), where \(\mathcal{H}_n\) is the Siegel half-space of degree \(n\). These kinds of Jacobi forms were systematically treated by \textit{C. Ziegler} [Abh. Math. Semin. Univ. Hamb. 59, 191--224 (1989; Zbl 0707.11035)]. In this paper the Selberg trace formula is described explicitly. An application yields an explicit formula of the dimension of the space of Jacobi cusp forms in the case \(n=2, k>l+4, l\) even.