We further develop the theory of W-graph ideals in a Coxeter system(W,S).We mainly study the structural coefficients of the corresponding modules,the direct and iterative algorithms for the canonical basis elements.Compared with standard recursive algorithms,this algorithm has the advantage of fast computation and memory saving when computing specific canonical basis elements.Due to the generality of the concept of W-graph ideal,our results are also the generalizations of those in some classical cases.