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In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A = FqT. We deduce closed-form expressions for traces of Hecke operators corresponding to primes of degree 1 and provide algorithms for primes of higher degree. We improve the Ramanujan bound and deduce the decomposition of cusp forms of level ₀ (T) into oldforms and newforms, as conjectured by Bandini-Valentino, under the hypothesis that each Hecke eigenvalue has multiplicity less than p.
Sjoerd de Vries (Fri,) studied this question.
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