Many studies adopt low-resolution, coarse-grained (CG) models to investigate polymers, proteins, and other soft materials. These studies must first specify the details that are retained in the low-resolution model, i.e., they must specify the “CG representation.” Unfortunately, the “best” representation for complex systems is not always obvious. In this study, we systematically explore the space of model representations for a typical protein and we examine how the properties of the CG model depend upon the choice of representation, i.e., the details retained in the CG model. By adopting a simple high-resolution model for protein fluctuations, we quantitatively assess the quality of a representation based upon its information content, I, and spectral quality, Q. While I quantifies the information lost due to eliminating details from the high-resolution model, Q quantifies the extent to which the representation preserves large scale motions. By employing these metrics as energy functions and adopting an ergodic move set, we explore the local and global minima in the space of representations. Additionally, by employing Monte Carlo methods, we quantify the number of representations with a given quality. We find that representations with high spectral quality match our physical intuition, while highly informative representations do not. Indeed, we find that the information content and spectral quality are anti-correlated among low-resolution representations. Moreover, our study suggests the possibility of a critical resolution below which there may exist a “phase transition” distinguishing good and bad representations. These studies may provide insight for developing CG models of soft materials and, more generally, for developing reduced representations of complex phenomena or high-dimensional data.