1. An image formation apparatus comprising: a storage portion to store a lookup table for converting first color data in a first color space having M dimensions (M is a positive integer) into second color data in a second color space having N dimensions (N is a positive integer); a reference lattice point setting portion to set, as a reference lattice point, a lattice point where M elements are each equal to or smaller than M elements of said first color data, of a plurality of lattice points in said first color space defined by said lookup table; a difference calculation portion to calculate, for each of M elements of said first color data, a difference from an element of a corresponding dimension of said reference lattice point, and to output a difference for each of M dimensions; a first setting portion to set said reference lattice point as a first process target lattice point; a process target dimension setting portion to set, as a process target dimension, a dimension having a largest difference of differences of dimensions not set as process targets of M dimensions; a second setting portion to set, as a second process target lattice point, a lattice point where an element of a dimension other than said process target dimension is equal to said first process target lattice point and the element of said process target dimension is larger than said first process target lattice point, of a plurality of lattice points in said first color space defined by said lookup table; a base term calculation portion to calculate a partial vector in said second color space, based on the difference of said process target dimension, said first process target lattice point, and said second process target lattice point; a resetting portion to reset said second process target lattice point as said first process target lattice point until a predetermined number (M−L) (L is a positive integer) of said partial vectors are calculated; a total sum vector calculation portion to calculate a total sum vector by adding up said partial vectors every time said partial vector is calculated; a reference vector calculation portion to calculate a second reference vector in said second color space corresponding to a first reference vector determined by a predetermined operational expression, using said lookup table, based on said second process target lattice point, differences of L dimensions, and L lattice points determined by said differences of L dimensions, after said process target dimension is set until the number of dimensions not set as said process target dimension by said process target dimension setting portion becomes L, and said second process target lattice point corresponding to a dimension set as the (M−L)th process target dimension by said second setting portion is set; and a conversion portion to calculate said second color data by adding said reference vector and a sum of said total sum vectors.