The derived Hecke algebra for dihedral weight one forms

Abstract

We study the action of the derived Hecke algebra in the setting of dihedral weight one forms, and prove a conjecture of the second- and fourth- named authors relating this action to certain Stark units associated to the symmetric square L-function. The proof exploits the theta correspondence between various Hecke modules as well as ideas of Merel and Lecouturier on higher Eisenstein elements.