Drinfeld cusp forms: oldforms and newforms.

Let p = (P) be any prime of F q [ t ] , let m be any ideal of F q [ t ] not divisible by p and consider the space of Drinfeld cusp forms of level m p , i.e. for the modular group Γ 0 (m p). Using degeneracy maps, traces and Fricke involutions we offer definitions for p -oldforms and p -newforms which turn out to be subspaces stable with respect to the action of the Atkin operator U P. We provide eigenvalues and/or slopes for p -oldforms and p -newforms and a condition to get the whole space of cusp forms as the direct sum between them. [ABSTRACT FROM AUTHOR]