Free modules of vector-valued modular forms and applications to Jacobi forms

Jialin Li, Haowu Wang, Bohan Zhang

The space $M(\rho ;\mathcal{E})$ of weakly holomorphic modular forms for a dimension-$r$ complex representation $\rho$ of ${\mathrm{SL}}_2(\mathbb{Z})$ with growth prescribed by $\mathcal{E…