This note derives dimension formulas for drinfeld cusp forms tied to harmonic cocycles, suggesting new insights with brauer characters.
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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Boeckle et al. (2025) studied this question.
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