hi there, as a general principle you should think about getting approximately 50 watt (real) per square foot.. so the 40x40 equals to about 1.7 sqft, so basically you don't want to go higher than 85w (real) in this size.
the plant eventually doesn't really care about what lamp she's under, as long as she get's a specific range of DLI (daily light integral) (yes, it's a bit simplified, as spectrum does play a bit of a role, but i'll leave this out for now), which for cannabis would be a minimum of 20 mol a day, or for best yield around 40 mols a day. more brings only diminishing returns with much higher cost of electricity, and then you'd also have to add extra co2 for the plant to be able to actually use that higher intensity..
How these 20 (min)/40 (best) mol per day are split up, depends on the light-cycle.. if you're running 18 hours through veg and bloom (as an auto), then this would attribute to a minimum of 308 micro-mol (umol) per second, or 617 umol/s in the best scenario for highest yield per power-ratio. this is basically the often-seen PPFD value that growers look at when comparing and testing grow-lights..
If you have a photoperiodic plant, then these 20 mol/40 mol would have to be divided up by 12 hours instead of 18, and then you'd be around 462 (minimum) umol/s or 925 umol/sec (optimal, but anything above around 850 umol/s requires co2 to be added).
I have a box with a similar grow area and use a 50w COB, and that's doing fine (see my "white haze" diary). And even at this intensity (due to the high PPFD because of the limited box height and the shorter distance after the stretch), i already supplement co2.
I was thinking of maybe putting a quantum board inside, but then i would definitely have to dim it down quite a bit, as otherwise the intensity will be too high if the plants get too close.
happy growing!