The general rule of thumb is 4 square feet per chicken in the coop - and 10 square feet per chicken in the run. However, that's not set in stone.
My chickens go into the coop to (1) roost at night - and (2) during the day to lay their eggs. The rest of the time (all daylight hours) they spend in the run. So for a coop and run the sizes you listed, you could probably have more than 4 chickens - IF they'll spend most of their time in the run. Using the "rule of thumb" measurement, at 10 square feet per chicken, your run is big enough for 11 chickens, but the coop only has room for 4. I think you could have 5 or 6 chickens since your run is large in comparison to the coop.
I once had 7 chickens in a 3 x 6 coop - which was considerably less than the recommended 4 square feet per chicken. However, they had MORE than enough room in there. They roosted all huddled together on one roosting pole - leaving the other pole empty. Then as soon as it was daylight, they headed out to the run and stayed there (with 10+ square feet per chicken) all day. They go to the coop to lay an egg, and then head right back out to the run. There was never any issues with overcrowding.
3, and even then you are going to be cleaning quite often and fighting ammonia build up.
I usually advise with the 5 sq./ft per bird in coop and 15 in run but I also advise that the minimum coop size should be considered first. INMPO 30 sq. ft is the minimum a coop should be period. You could then apply the 5' per bird and that would allow 6. Many people dont agree with me and that is ok, I can only speak from my experience. The main culprit when you get into a coop that small and max it out is problems keeping it clean and ammonia free.
I have 8 in a 3x5 coop now ( building bigger in spring) but they spend most time in the 10x10 dog pen that the coop is in, ( raised off the ground 3 ft) and I let them free range as much as I can, but I dont let them out of the pen when I am not home
Bairo has a good point about frequent cleaning on a small coop. When I had 7 chickens in the 3 x 6 coop, I had to clean it at least once a week. It was an easy coop to clean, though, so it wasn't a big deal. I have a 10 x 20 coop now with an even larger run. So that smaller coop/run will be used as a breeder, brooder or isolation pen.
So much depends on the design - and how easily the run is accessed - and if the chickens free range at all. If they stay in the coop/run 24/7, get fewer birds. If they free range for an hour or two each day, then you can have more.
I think you have to watch the behavior of your chickens, too. If they're crowded there will be more pecking and bullying-type behavior.