This paper investigates the language dominance hypothesis in multilingual large language models (LLMs), which posits that cross-lingual understanding is facilitated by an implicit translation into a dominant language seen more frequently during pretraining. We propose a novel approach to quantify how languages influence one another in a language model. By analyzing the hidden states across intermediate layers of language models, we model interactions between language-specific embedding spaces using Gaussian Mixture Models. Our results reveal only weak signs of language dominance in middle layers, affecting only a fraction of tokens. Our findings suggest that multilingual processing in LLMs is better explained by language-specific and shared representational spaces rather than internal translation into a single dominant language.