What is this copper compound I made? I started with copper (II) sulfate solution left over from a recrystallization. I added sodium carbonate (definitely an excess) and about 200 of water and got a lot of bubbling. I heated it, for no particular reason. Few hours later I filtered the solution, which now looked dingy gray. I got a deep blue solution with a pH of around 11, and what was in the filter was black...

The filtrate is still deep blue with no precipitate, I'm washing and drying the residue from the filter, but I'm still curious what I made. I should have gotten basic copper carbonate, I've done this before to get copper carbonate, I can't remember if I've used sodium carbonate or bicarbonate last times though. I didn't think it made a difference.
There are two surprising phenomena in this experiment.

First : $\ce{CuSO_4}$ reacts in a unusual way with $\ce{Na_2CO_3}$. The equation is :  $$\ce{2 CuSO_4 + 2 Na_2CO_3 + H_2O -&gt; Cu(OH)_2·CuCO_3 + CO_2 + 2 Na_2SO_4}$$ This forms some bubbles of $\ce{CO_2}$ as you have seen. And it produces a strange precipitate of the so-called basic copper carbonate, $\ce{Cu(OH)_2·CuCO_3}$, which is well known in geology as the mineral called malachite. This formula is sometimes written as $\ce{Cu_2CO_3(OH)_2}$. This is what you have obtained as your insoluble deposit.

Second : Basic Copper carbonate gets redissolved in a big excess of carbonate ions, producing a deep blue solution containing an anion which is probably $\ce{[Cu(CO_3)_2]^{2-}}$ This is what you have obtained in your blue filtrate.