A basis of 𝑆 4 ( Γ 0 ( 4 7 ) ) is given and the formulas for the number of representations of positive integers by some direct sum of the quadratic forms 𝑥 2 1 + 𝑥 1 𝑥 2 + 1 2 𝑥 2 2 , 2 𝑥 2 1 ± 𝑥 1 𝑥 2 + 6 𝑥 2 2 , 3 𝑥 2 1 ± 𝑥 1 𝑥 2 + 4 𝑥 2 2 are determined.