Atkin–Lehner theory for Drinfeld modular forms and applications

Abstract

The present paper deals with Atkin–Lehner theory for Drinfeld modular forms. We provide an equivalent definition of \(\mathfrak {p}\)-newforms (which makes computations easier) and commutativity results between Hecke operators and Atkin–Lehner involutions. As applications, we show a criterion for a direct sum decomposition of cusp forms, we exhibit \(\mathfrak {p}\)-newforms arising from lower levels and we provide \(\mathfrak {p}\)-adic Drinfeld modular forms of level greater than 1.