COLEMAN'S L-INVARIANT AND FAMILIES OF MODULAR FORMS

We prove the conjecture of Mazur, Tate, and Teitelbaum with Coleman's L-invariant for a newform f of arbitrary weight k(0) >= 2 of split multiplicative type at a prime p > 2. The key step in the proof is to show that Coleman's L-invariant is given by L(f) = -2p(k0/2)alpha'(k(0)), where alpha(k) is the eigenvalue of U(p) acting on the germ of a Coleman family f(k) passing through f at k = k(0).