Bo-Han Zhang

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

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 $\mathcal{E}$ at the cusp is a free module over $\mathbb{C}[E_4,E_6]$. We first prove that a $\mathbb{C}[E_4,E_6]$-linearly independent homogeneo...