Let f be a Drinfeld modular form of level Γ0(m) which is an eigenform for the Hecke operator Tp (p a prime of Fq[T]). We study the relations between the Fourier coefficients of f and the p-adic valuation of its eigenvalue (slope). We use formulas for some of the Fourier coefficients of Tpf to provide bounds and estimates on the slopes and, in particular, to find necessary conditions for “large” slopes, whose existence is closely connected with conjectures on oldforms and newforms.
Fourier coefficients and slopes of Drinfeld modular forms
Andrea Bandini
;
2023-01-01
Abstract
Let f be a Drinfeld modular form of level Γ0(m) which is an eigenform for the Hecke operator Tp (p a prime of Fq[T]). We study the relations between the Fourier coefficients of f and the p-adic valuation of its eigenvalue (slope). We use formulas for some of the Fourier coefficients of Tpf to provide bounds and estimates on the slopes and, in particular, to find necessary conditions for “large” slopes, whose existence is closely connected with conjectures on oldforms and newforms.File in questo prodotto:
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