Whether you can fine-tune a model depends less on its size than on how many of its parameters you train and how many bits you store the rest in. A 7-billion-parameter model needs over 80 GB to fine-tune fully and about 5 GB with a quantised base and LoRA adapters.
You will find that configuration, then write the two formulas that make the estimate: the number of LoRA parameters and the training memory.