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Adelic formulations of complex multiplication and modular curves

This is an expansion of my comment above: You can view the modular curve of level $K$ over $\mathbb{C}$ as the double coset space $$GL_2(\mathbb{Q})\backslash\mathbb{H}^{\pm}\times GL_2(\mathbb{A}_f)/ …
Keerthi Madapusi's user avatar