Training a deep learning model on source code has gained significant traction recently. Since such models reason about vectors of numbers, source code needs to be converted to a code representation before vectorization. Numerous approaches have been proposed to represent source code, from sequences of tokens to abstract syntax trees. However, there is no systematic study to understand the effect of code representation on learning performance. Through a controlled experiment, we examine the impact of various code representations on model accuracy and usefulness in deep learning-based program repair. We train 21 different generative models that suggest fixes for name-based bugs, including 14 different homogeneous code representations, four mixed representations for the buggy and fixed code, and three different embeddings. We assess if fix suggestions produced by the model in various code representations are automatically patchable, meaning they can be transformed to a valid code that is ready to be applied to the buggy code to fix it. We also conduct a developer study to qualitatively evaluate the usefulness of inferred fixes in different code representations. Our results highlight the importance of code representation and its impact on learning and usefulness. Our findings indicate that (1) while code abstractions help the learning process, they can adversely impact the usefulness of inferred fixes from a developer's point of view; this emphasizes the need to look at the patches generated from the practitioner's perspective, which is often neglected in the literature, (2) mixed representations can outperform homogeneous code representations, (3) bug type can affect the effectiveness of different code representations; although current techniques use a single code representation for all bug types, there is no single best code representation applicable to all bug types.