An antireflection or light-absorbing coating composition which exhibits good light absorption in the wavelength range of from 100 to 450 nm, is free from footing and intermixing, and possesses excellent storage stability and step coverage; and a novel copolymer therefor. The copolymer is an acrylic or methacrylic copolymer comprising a main chain having carboxyl groups bonded to the carbon atoms thereof and, reaction-bonded thereto, at least (1) repeating units each comprising an aminated or hydroxylated organic chromophore which absorbs light in the wavelength range of from 100 to 450 nm directly or through and -R1NHCXY- group (wherein R1 represents an alkylene group; X represents O or S; Y represents O or an NR6 group; and R6 represents H or a substituted or unsubstituted, straight-chain or cyclic alkyl or phenylene group), and (2) repeating units each comprising an alkyl group having a double bond or an epoxy group. A resist image having high resolution can be formed by coating a wafer with the above composition to form a bottom antireflection coating, coating the surface of the coating with a photoresist, and then conducting exposure to far ultraviolet light and development.