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 the ideas of Merel and Lecouturier on higher Eisenstein elements.
To Gopal Prasad on his 75th birthday
"The Derived Hecke Algebra for Dihedral Weight One Forms." Michigan Math. J. 72 145 - 207, August 2022. https://doi.org/10.1307/mmj/20217221