Let $\mathbb{A}$ be the ring of adeles. Let $N$ be a natural number. Let $\Gamma(N)=\ker(\text{SL}_2(\mathbb{Z})\rightarrow\text{SL}_2(\mathbb{Z}/N\mathbb{Z})))$.
I saw the following embedding of $\text{SL}_2(\mathbb{R})$-modules mentioned:
$\varphi:L^2(\Gamma(N)\backslash\text{SL}_2(\mathbb{R})) \hookrightarrow L^2(\text{SL}_2(\mathbb{Q})\backslash \text{SL}_2(\mathbb{A})))$
The only reference was to the "Strong Approximation Theorem". I tried to look it up, but it was hard for me to understand the references and their relation to this embedding.
What is the embedding $\varphi$?