The structure of Drinfeld modular forms of level ${\Gamma }_0(T)$ and applications

Abstract

In this article, we describe the structure of the $R$-algebra of Drinfeld modular forms $M({\Gamma }_0(T){)}_R$ (resp., $M^0({\Gamma }_0(T){)}_R$) of level ${\Gamma }_0(T)$ and the structure of mod-$\p$ reduction of $M_{\mfp}^0(Γ_0(T))$ for $\p \neq (T)$. As a result, we are able to study the properties of the weight filtration for $M_{k,l}({\Gamma }_0(T))$. Finally, we prove a result on mod-$\p$ congruences for Drinfeld modular forms of level $Γ_0(\p T)$ for $\p \neq (T)$.

References in corpus (1)

• On mod $\mathfrak{p}$ congruences for Drinfeld modular forms of level $\mathfrak{pm}$