# Jacobi forms of theta type

## TL;DR

This paper introduces theta type Jacobi forms associated with positive definite even lattices, constructs three towers of such forms with a simple pullback structure, and explains the existence of a specific cusp form related to the $D_4$ lattice.

## Contribution

It defines theta type Jacobi forms for lattices, constructs new towers of these forms, and links them to a special cusp form with symmetries of the $D_4$ lattice.

## Key findings

- Constructed three towers of theta type Jacobi forms
- Established a pullback-structure for these forms
- Explained the existence of a weight 24 cusp form for $D_4$

## Abstract

Let $L$ be a positive definite even lattice. We introduce theta type Jacobi forms and construct three towers of Jacobi forms with a particular easy pullback-structure. We use theta type Jacobi forms to explain the existence of a cusp form of weight 24 with respect to the irreducible root lattice $D_{4}$ which is based on additional symmetries of the Coxeter diagram.