Short Term Capital Gains Losses Carryover

Hi,

 

For the year 2020, I had a collective short term capital gains loss of $10,000. As far as I understand it, only $3,000 can be deducted in a given year with the remainder ($7,000) carrying forward to subsequent years. I just wanted to confirm a couple of things, is there any special form that I need to fill out for the year 2020 and in 2021 if my short term capital gains theoretically are $8,000, would the $7,000 that was carried over be deducted from that total or would it still only be limited to $3,000 in a given calendar year? And on the flip side, if I incur additional short term capital gains losses in 2021, would that simply be added to the $7,000 that was carried over? And in either scenario, would there be any additional forms I would have to fill out in 2021 due to that losses that were carried over?