Answer
The conjugate base of $H_2CO_3$ is $HC{O_3}^-$
Work Step by Step
To find the conjugate base of an acid, just remove one proton $(H^+)$ from the compound.
1. Remove one hydrogen:
$H_2CO_3 -- \gt HCO_3$
2. Subtract one from the charge
$0 --\gt -1$
$H{CO_3} -- \gt HC{O_3}^-$