A certain level-index changing operator on Jacobi cusp new forms

Let $N$ be an odd square-free integer. We give a Hecke isomorphism map from the space of Jacobi cusp new forms of level $1$ and index $N$ satisfying a certain condition into the space of Jacobi cusp new forms of level $N$, index $1$ and the character after reviewing about some known properties of level-index changing operators.