Abstract
Let [Formula: see text] be a Drinfeld modular form of level [Formula: see text] which is an eigenform for the Hecke operator [Formula: see text] ([Formula: see text] a prime of [Formula: see text]). We study the relations between the Fourier coefficients of [Formula: see text] and the [Formula: see text]-adic valuation of its eigenvalue (slope). We use formulas for some of the Fourier coefficients of [Formula: see text] 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.
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