I'm interested in locating dimension formulae for (more general) Jacobi forms associated with a lattice $L$ (where the Jacobi forms of Eichler-Zagier correspond to $L=A_1$).

Unfortunately, the literature seems rather diffuse and I'm rather hoping someone might be able to point me in the direction of some references.

When $L=A_1$, there are formulae due to Eichler-Zagier (and for the scaling $L=A_1(m)$ due to Skoruppa / Skoruppa-Zagier).

However, for general $L$ there seem to be far fewer results. In fact, I'm only aware of the 1992 results of Arakawa, who relates the dimension of spaces of Jacobi cusp forms to the orders of zeros of the Selberg Zeta function. This seems surprising: are there any more?