I am running IntelliJ IDEA on my macOS Big Sur and ⌃ + space for basic complete does not seem to work. I looked under Preferences / Keymap / Code Completion / Basic, and it seems in order.
Any ideas?
Found out that the OS itself has this already taken.
I disabled the shortcut on System Preferences -> Keyboard -> Shortcuts -> Input Sources -> Tick off "Select the previous input source" and it did the trick.