The structure of Drinfeld modular forms of level $Γ_0(T)$ and applications

In this article, we describe the structure of the $R$-algebra of Drinfeld modular forms $M(Γ_0(T))_R$ (resp., $M^0(Γ_0(T))_R$) of level $Γ_0(T)$ 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 $M_{k,l}(Γ_0(T))$. Finally, we prove a result on mod-$\p$ congruences for Drinfeld modular forms of level $Γ_0(\p T)$ for $\p \neq (T)$.

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