2. (8 points) This year is 2014, and 2014 is not a perfect square, but the digits can be rearranged to form a new four-digit number that is a perfect square, for example, $1024=32^{2}$. It is known that using the digits $2, 0, 1, 4$ once each, another four-digit perfect square can be formed. What is this new four-digit perfect square? $\qquad$ .
【Analysis】First, find the numbers whose last digit can only be 1 or 4 to form a perfect square. Then enumerate these numbers and factorize them. If any factor is not a perfect square, it does not meet the requirement.

【Solution】Solution: First, based on the judgment of being a perfect square, the last digit can be 1 or 4. There is no perfect square with a last digit of 2. When the last digit is 1 or 4, there are $1024, 1204, 2014, 2104, 2041, 2401, 4201, 4021$ for a total of 8 numbers.

Factorizing the above 8 numbers, we get:
(1) $1024=2^{5}$, (2) $1204=4 \times 301$ (does not meet the requirement), (3) $2014=2 \times 1007$ (does not meet the requirement), (4) 2104 $=8 \times 263$ (does not meet the requirement)
(5) $2041=13 \times 157$ (does not meet the requirement), (6) $2401=49^{2}$ (meets the requirement), (7) 4201 (prime number), (8) 4021 (prime number).

Therefore, the answer is: 2401