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arXiv · 1908.09768

On Drinfeld cusp forms of prime level

Andrea Bandini·Maria Valentino
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Abstract

Let $(P_d)$ be any prime of $\mathbb{F}_q[t]$ of degree $d$ and consider the space of Drinfeld cusp forms of level $P_d$, i.e. for the modular group $Γ_0(P_d)$. We provide a definition for oldforms and newforms of level $P_d$. Moreover, when the dimension of the vector space of oldforms is one and $P_1=t$ we prove that the space of cuspforms of level $t$ is the direct sum of oldforms and newforms and that the Hecke operator $\mathbf{T}_t$ acting on Drinfeld cusp forms of level 1 is injective, thus providing more evidence for the conjectures presented and stated in [2] and [3].

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Andrea Bandini, Maria Valentino. 2019-08-26. On Drinfeld cusp forms of prime level. https://arxiv.org/abs/1908.09768

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