I'm planning on sending a colony ship on an extended, multi-generational voyage to a distant star. My colony ship is an oblate spheroid, 2km long on its long axis and 1km across on its shortest access. It's built using near future technology, with power generation provided by fusion plants and thrust via a large array of solar sails, which are mounted on external control pods and don't take up much of the 'internal' space on the ship. The sails can expand to an enormous area, but primarily use albedo changes to move around based on solar pressure, so their control doesn't heavily tax the power supply systems on the ship.
Internally, I've got my power generation systems located along the central axis of the ship, with all technical areas and industry clustered around those. Following my industrial section, which must produce and recycle all goods for the populace of my ship, I've got habitation and commerce modules wrapping around the core in cylindrical layers, with farms and natural areas forming the outermost layers. I'm expecting the natural areas to be responsible for the majority of organic recycling and air filtration on the ship, though there is a backup system of atmospheric scrubbers to maintain a breathable atmosphere in the event of a biological breakdown in the nature modules. The entire ship is close to a zero-g environment, with the exception of several exercise modules, which generate artificial gravity by rotating around the rest of the ship. These gently rotate the rest of the ship, in accords with conservation of angular momentum, resulting in very gentle gravity acting on the rest of the ship, which leads to objects slowly settling towards the 'up' direction over the course of several minutes.
The voyage is expected to take at least several centuries, so most systems on the ship will need to be replaced/maintained via onboard facilities multiple times. Technology has progressed to the point where the most space efficient way to handle this is by recycling all materials, rather than by carrying spare parts, though manufacturing methods are still broadly similar to what we have today, rather than using nanobots or the like.
If I pack all of my essential systems in as efficiently as possible, about how many colonists can I expect to fit on board my ship?