Let p=(P) be any prime of Fq[t], let m be any ideal of Fq[t] not divisible by p and consider the space of Drinfeld cusp forms of level mp, i.e. for the modular group Γ0(mp). 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 UP. 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.
Drinfeld cusp forms: oldforms and newforms
Bandini A.;Valentino M.
2022-01-01
Abstract
Let p=(P) be any prime of Fq[t], let m be any ideal of Fq[t] not divisible by p and consider the space of Drinfeld cusp forms of level mp, i.e. for the modular group Γ0(mp). 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 UP. 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.File in questo prodotto:
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