Assemblies of plasmonic nanoparticles possess exotic properties that are used in numerous applications. Their efficiency for specific applications strongly depends on the modes supported by the structure. In this paper, we extend the Green's tensor formalism to compute the eigenmodes of an assembly of plasmonic nanoparticles. Using the developed technique, we investigate the specific cases of a nanoparticle monomer, dimer, and trimer. The influence of various geometrical parameters and of symmetry breaking on the eigenmodes of the assemblies is studied in detail, as well as the illumination conditions required to excite specific eigenmodes.