Below is a matrix diagram, produced in Mathematica. In this case it's a $956\times 950$ rectangular matrix. The white parts are all zero.

```
sa = Import["https://pastebin.com/raw/fiErKrhU", "Package"];
MatrixPlot[sa]

```

[![MatrixPlot](https://i.stack.imgur.com/bZYNH.png)](https://i.stack.imgur.com/bZYNH.png)

I'm wondering if there is a way to efficiently compute the null space of this matrix. From a different calculation entirely (using a Molien series), I know in advance there should be 6 linearly independent vectors in this null space, and I already know one of them.

The `NullSpace` routine takes too long to be feasible. I am hoping that there is a better way. I know that using `NullSpace[N[m]]` will return the answer rather quickly, but I am hoping to be able to do this symbolically.

Any help would be appreciated.

Update
------

Added `SparseArray` data for this matrix. It was too large for this message so I put it on pastebin.

<https://pastebin.com/raw/fiErKrhU>