The following:
TemplateBox[{"a", "b"}, "Binomial"] // RawBoxes
yields the correctly formatted (2d box structure) of Binomial[a,b]:
$$\begin{pmatrix}a\\b\end{pmatrix}$$
But I would like to see its (and other built-in functions') explicit definition in terms of low level boxes. Presumably, the definition of the style "Binomial"
lives somewhere. Where is it?