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

Let p ∈ { 3 , 5 , 7 } and let Δ denote the weight twelve modular form arising from Ramanujan’s tau function. We show that Δ is congruent to an Eisenstein series E k , χ , ψ modulo p for explicit choices of k and Dirichlet characters χ and ψ . We then prove formulae describing the Iwasawa invariants of the Mazur–Tate elements attached to Δ , confirming numerical data gathered by the authors in a previous work.