Neutrals: you could paint with white, cream, or pale stone, browns or beige
Mauve: try different shades of mauves, lilacs and purples, to co-ordinate with the carpet
Lemon/Pale yellow: the opposite color on the color wheel to mauve is a pale lemon. This will give quite an interesting contrast to the carpet, but will 'harmonise' quite nicely with the oranges and reds of the brick fireplace too. A deeper yellow may also work well, but this may depend on the size of your room, as yellow can be quite a strong color in a room - although gives a very cheerful feel.
Greens: Greens make up the third part on the color wheel in a 'triadic scheme', with a combination of mauves (purple) and oranges/reds (for the brick). Green can be a lovely restful color for a room, very calming! Pale greens will make a room feel larger.
If you are concerned over the exact tones and shades of each color that might go, consult a color wheel to get an exact shade, which you can then match up to a paint .... or just try out tester pots of color combinations on your wall (always a good plan in any case)!
I hope this has been some help to you in making your decision, happy decorating!
