Some call it solenoid G or 7 here is what it does
Modulated main pressure solenoid (7) is a normally closed solenoid used to modulate the transmission main pressure. Under specific conditions, such as low throttle setting, low engine torque, low engine speed, and low transmission output speeds, the transmission control module (TCM) commands the solenoid on. When the solenoid is applied, fluid is routed to the main pressure regulator valve; this in turn reduces the main pressure schedule and improves the volume of oil through the overage circuit. By modulating main pressure, the cooler flow at idle can be increased allowing improved cooling and reducing transmission pump noise.