I like white and blue rooms too. They are so fresh and blue never dates, it always seems to be in fashion

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I assume being a basement the ceilings aren't high and it probably doesn't have a lot of natural light. To make a space look bigger I would have light coloured floors, walls and ceilings. I would have any mouldings or trims the same colour as the walls so as not to break up the space. I would use a light bone colour on the walls and floor and a white ceiling - if you have some natural light in the basement. The less light you have the paler I would make the floors and walls.
I like the idea of a a white & black & purple room.
So with the pale walls, floor and ceiling and the purple couch. I suggest black as an accent colour. So maybe black & white photos, if the room is used as a TV room maybe black and white pictures of movie stars. I would have large white mats/mounts on the pictures and black frames. Some black or black & purple patterned cushions.
I am not sure about the red rug. I think it would look very fashionable to have a black and white rug maybe with some geometrical pattern.
I would use purple in some of your accessories such as a lamp shade, candles. flowers, vases, platters etc.
Let us know if we are on the right track
This room I found in a great blog called
www.apartmenttherapy.com might help you visualise the room