  The $10^+$ and $27/2^-$ isomers of the $Z>64$, $N=82$ nuclei are investigated
in the shell model framework. We derive an extended seniority reduction formula
for the relevant $E2$ transition strengths. Based on the extended formula, as
well as on the approximate degeneracy among the $0h_{11/2}$, $2s_{1/2}$ and
$1d_{3/2}$ orbits, we argue that the $B(E2)$ data require the $^{146}$Gd core
excitation. The energy levels of both parities and the $B(E2)$ values are
simultaneously reproduced by a multi-$j$ shell model calculation with the MSDI,
if the excitations from $(0g_{7/2}1d_{5/2})$ to $(0h_{11/2}2s_{1/2}1d_{3/2})$
are taken into account.
