Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series

Anthony Doyon, Antonio Lei

Let $p\in \{3,5,7\}$ and let $\hat{I}”$ denote the weight twelve modular form arising from Ramanujan's tau function. We show that $\hat{I}”$ is congruent to an Eisenstein series $E_{k,\ddot{I}‡,\ddot{I}ˆ}$…