How is it possible for white dwarf stars to have lower luminosity than the sun even though the sun is cooler than white dwarfs?

Hint: When reactions taking place on a star, which enables it to generate its own electromagnetic radiation cease on a star, it becomes a white dwarf star. The sun is still a star; this means chain reactions take place on its surface. A dwarf star is smaller than the sun but very hotter.

Complete step-by-step solution:
The electromagnetic radiation given out by stars like the sun is due to continuous nuclear chain reactions of fission of four hydrogen atoms combining to form one helium atom.
There comes a point when these reactions stop because no more atoms are there to take part in the reactions of the atoms that get exhausted.
When these reactions stop completely, stars like the sun become white dwarf stars. When the nuclear reactions cease, their outer material is expelled by the stars, and only the inner core is left. The inner core is extremely hot with a temperature up to 100,000 K. Therefore the size of the star considerably decreases.
White dwarf stars have a smaller size than the sun, also the sun is continuously generating energy while the dwarf stars can no longer generate any energy that is why the white dwarf planets have less luminosity than the sun.
Therefore, the white dwarf stars have less luminosity than the sun because of their small size also because they are not able to generate their own energy as the chain fusion reactions have ceased on their surface.

Note: The outer material expelled by the dwarf stars is called nebula and the material is mostly ionized gases. The density of a dwarf star is about 200,000 times more than the Earth. White dwarf stars are only left with the inner core of a star. When the reactions will cease on the sun, it will also become a white dwarf star.