In this study, when the field characteristic is 13, we calculate decomposition matrices for the spin characters   and   which are broken down into blocks, where the decomposition matrices are connected between irreducible spin characters and irreducible modular spin characters. The technique used in this study is -inducing, which produces projective characters for symmetric group  by projecting 's character, and symmetric group  by projecting 's character. We can find it by fixing all bar divisions, finding all irreducible spin characters for  ( ), , and all irreducible modular spin characters for  ( ), . In order to explore irreducible modular spin characteristics, general correlations and theorems will be discovered as a result of this research.