The structure of the hydrated electron, which is a key species in radiative processes in water, has remained elusive. The traditional cavity model has been questioned recently, but the newly suggested picture of an electron delocalized over a region of enhanced water density is controversial. Here, we present results from ab initio molecular dynamics simulations, where not only the excess electron but also the valence electrons of the surrounding water molecules are described quantum mechanically. Unlike in previous one-electron pseudopotential calculations, many-electron interactions are explicitly accounted for. The present approach allows for partitioning the electron solvated in liquid water into contributions from an inner cavity, neighboring water molecules, and a diffuse tail. We demonstrate that all these three contributions are sizable and, consequently, important, which underlines the complex nature of the hydrated electron and warns against oversimplified interpretations based on pseudopotential models.