On certain vector valued Siegel modular forms of type $(k,2)$ over $\mathbb Z_{(p)}$
Volume 188 / 2019
Acta Arithmetica 188 (2019), 83-98
MSC: Primary 11F46; Secondary 11F30.
DOI: 10.4064/aa171119-21-5
Published online: 14 February 2019
Abstract
We give generators of the module over $M_*^{{\rm ev}}$ of vector valued Siegel modular forms of type $(k,2)$ over $\mathbb Z_{(p)}$. This gives an example of the positive solution to the more general problem whether the module of vector valued modular forms of arbitrary degree is finitely generated over the ring of modular forms for $\mathbb Z_{(p)}$.
