  We establish an effective version of the Andr\'e-Oort conjecture for linear
subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. Apart
from the trivial examples provided by weakly special subvarieties, this yields
the first algebraic subvarieties in a Shimura variety of dimension $> 1$ whose
CM-points can be (theoretically) determined.
