Dimension formulas for certain spaces of Drinfeld cusp forms
Abstract
In this short note, we derive dimension formulas for spaces of Drinfeld cusp forms corresponding to harmonic cocycles invariant under the group SL2(Fq[t]) and with values in absolutely irreducible SL2(Fq(t))-representations via the theory of Brauer characters. This generalizes results in [BGP21] obtained by different methods. In addition, we prove a simple asymptotic formula for these dimensions.
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