How to find the radical of this Lie algebra

Question

Let $k$ be a field, and for $1 < m < n, \ $ let $\ \mathfrak{g}_m = \{ (a_{ij})_{ij} \in \mathfrak{gl}(n,k): a_{ij} = 0 \text{ for } i > m\}.$ What is the radical of $ \mathfrak{g}_m$? I tried working it out for small values of $n$ and $m$, but otherwise I'm stuck.