Greenberg's $\mathcal{L}$ -invariants of adjoint square Galois representations

For a two-dimensional p-adic Galois representation V associated to a p-ordinary Hecke eigen cusp form f of weight k ≥ 2, we identify the $\mathcal{L}$ -invariant (of Greenberg) of the (three-dimensional) adjoint square Ad(V) of V with the derivative of the p-coefficient of the Λ-adic lift of f. By this result, for a given p-adic analytic family of ordinary Hecke eigenforms, the $\mathcal{L}$ -invariant does not vanish for almost all members in the p-adic family (as expected).