## STNB2019 (33rd edition)

### Proof of Venkatesh’s conjecture for dihedral weight one forms.

#### Abstract

We will sketch the proof of Venkatesh’s conjecture for dihedral weight one forms, focussing on the case where $g$ is the theta series of a Hilbert class character of an imaginary quadratic field $K$. The main tools are Mazur’s classical results on the Eisenstein ideal and Merel-Lecouturier’s theory of higher Eisenstein elements.