15. In the Cartesian coordinate system $x O y$, there are parabolas $C_{i}: y=a_{i} x^{2}+b_{i} x+c_{i}(i=1,2, \cdots, 20)$, and parabolas $D_{j}: x=$ $a_{j}^{\prime} y^{2}+b_{j}^{\prime} y+c_{j}^{\prime}(j=1,2, \cdots, 20)$. For any real numbers $a_{i}, b_{i}, c_{i}, a_{j}^{\prime}, b_{j}^{\prime}, c_{j}^{\prime}$, the maximum number of regions into which these 40 parabolas can divide the coordinate plane is $\qquad$.
The parabolas $C_{i}$ intersect each other at most 2 points, so parabola $C_{1}$ divides the coordinate plane into 2 regions, $C_{2}$ intersects with $C_{1}$ at most 2 points, these 2 points divide $C_{2}$ into 3 segments, each segment divides the region it is in into two, thus $C_{1}$ and $C_{2}$ divide the coordinate plane into at most $2+3=5$ regions;
Parabola $C_{3}$ intersects with $C_{1}, C_{2}$ at most 4 points, these 4 points divide $C_{3}$ into 5 segments, each segment divides the region it is in into two, thus $C_{1}, C_{2}, C_{3}$ divide the coordinate plane into at most $2+3+5=10$ regions; and so on, $C_{1}, C_{2}, \cdots, C_{20}$ divide the coordinate plane into at most $2+3+5+\cdots+39=401$ regions. Similarly, $D_{1}, D_{2}, \cdots, D_{20}$ divide the coordinate plane into 401 regions.
Furthermore, parabola $C_{1}$ intersects with each of $D_{j}$ at most 4 points, so the total number of intersection points between $C_{1}$ and $D_{1}, D_{2}, \cdots, D_{20}$ is at most 80 points, these 80 points divide $C_{1}$ into 81 segments, each segment divides the region it is in into two, i.e., it can add at most 81 new regions, thus the intersection points between $C_{i}(i=1,2, \cdots, 20)$ and $D_{1}, D_{2}, \cdots, D_{20}$ can add at most $81 \times 20=1620$ new regions.
Therefore, the 40 parabolas divide the coordinate plane into at most $401+401+1620=2422$ regions.