  We study the variation of $\mu$-invariants of modular forms in a cuspidal
Hida family in the case that the family intersects an Eisenstein family. We
allow for intersections that occur because of "trivial zeros" (that is, because
$p$ divides an Euler factor) as in Mazur's Eisenstein ideal paper, and pay
special attention to the case of the 5-adic family passing through the elliptic
curve $X_0(11)$.
