Turtles generate a lot of waste. I 'baby-sat' a rescued red-ear for a week, and couldn't believe how quickly he fouled the water. I don't think a small sponge will do it, unless you are also committed to changing out the bulk of the water every other day or so. I don't know much about turtles and biofiltration; the one good thing is that you can always change out the water without being as finicky about the parameters as you do with fish.
Hopefully, another turtle owner will chime in.
well, i've had mine for 10 years, I just wasn't sure if there was anything dif for the 40g of water, right now he only has about 10g of water in a 30g aquarium, I have run it off an UGF for ten years, but now I'm moving him into an environment more appropriate for him where he'll have about 4 times the living and swimming space