how deep can a p-trap go into bsmt floor

shower is 2" drain and i want to vent with 2" as well, the sewer line is 11" deep in the cement floor, can i lower my trap below the sewer line then come up to the vent and slope down to the sewer from there, this is so i can fit everything under the new floor

thanks for your help

From the outlet of the p-trap, you can only go down. That means that the bottom of the p-trap will be below the drain line.

will vent work properly

what i want to do is go a foot to sixteen inches straight down from shower drain, hook on semi-circular curved part of trap, then travel straight up and connect to elbow outlet of trap at a height that would allow me to connect the vent so it will be under the floor at a decent height above the sewer drain line ( which is 11" under cement), from the vent i have to travel about 10' to the sewer drain
i could put the trap even deeper if allowable, just want to confirm that vent will still work if i do so

You don't want to do that...the trap being that deep first means you'll have a change for accumulation of crud in the pipe that you'll smell and have to clean and, a trap that deep just won't work properly. You can run your vent up from the drain line within the allowances if you set the trap to what you have now.