Fluid antenna systems (FASs) have introduced a new paradigm for wireless system design by revealing how mutual correlation can be exploited to harvest inherent spatial diversity. While existing studies have mainly focused on one-sided FAS configurations, i.e., with FAS deployed at either the transmitter or the receiver, this work investigates the ergodic capacity of a jointly correlated dual-side FAS under statistical eigenmode transmission. Specifically, a jointly correlated dual-side channel model is developed, and the corresponding ergodic capacity together with a tight closed-form upper bound is derived. In addition, the optimal power allocation is studied, and a practical iterative algorithm is proposed for its implementation.