A new theta cycle for $GSp_4$ and an Edixhoven type theorem

In this paper, we investigate a new theta cycle for $GSp_4/\mathbb{Q}$ by using author's theta operators defined in the previous work. In the course of the construction, we also modify the theta operators so that they work in any characteristic, including $p = 2$, and for any weight. As an application, we discuss an Edixhoven type theorem for $GSp_4/\mathbb{Q}$.