Automated Program Repair (APR) has evolved significantly with the advent of Large Language Models (LLMs). Fine-tuning LLMs for program repair is a recent avenue of research, with many dimensions which have not been explored. Existing work mostly fine-tunes LLMs with naive code representations and is fundamentally limited in its ability to fine-tune larger LLMs. To address this problem, we propose RepairLLaMA, a novel program repair approach that combines 1) code representations for APR and 2) the state-of-the-art parameter-efficient LLM fine-tuning technique called LoRA. This results in RepairLLaMA producing a highly effective `program repair adapter' for fixing bugs with language models. Our experiments demonstrate the validity of both concepts. First, fine-tuning adapters with program repair specific code representations enables the model to use meaningful repair signals. Second, parameter-efficient fine-tuning helps fine-tuning to converge and contributes to the effectiveness of the repair adapter to fix data-points outside the fine-tuning data distribution. Overall, RepairLLaMA correctly fixes 125 Defects4J v2 and 82 HumanEval-Java bugs, outperforming all baselines.