when viewing the nerdtree window, how can i widen it?

In the Vim vocabulary what you call a "pane" is actually a "window" and the window you want to resize has nothing particular so :h window-resize should give you all you need, especially:

                        *CTRL-W_>*
CTRL-W >    Increase current window width by N (default 1).

So ctrl+w> will increase the window size once and 10ctrl+w> will do the same thing 10 times.

If you need to change the size in a script you want to read :h :wincmd which allows you do to the same thing as the ctrl+w normal commands.

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Also :copen probably doesn't do what you think: it opens a window containing the quickfix list. If you want to open a vertical split you probably want :split or ctrl+ws