For hyperelliptic curves and curves of genus less than 2, the canonical map is not an embedding. For modular curves $X_G$ of this form, we take the lowest even weight $k$ so that Riemann-Roch guarantees an embedding into the projectivization of the space of modular forms associated to $G$. We refer to the image of this embedding as the embedded model of $X_G$.
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- Last edited by David Roe on 2023-01-02 17:29:24