Osman Bizim

On the number of representations of positive integers by quadratic forms as the basis of the space S4(Γ0(47),1)

The number of representations of positive integers by quadratic forms F 1 = x 1 2 + x 1 x 2 + 12 x 2 2 and G 1 = 3 x 1 2 + x 1 x 2 + 4 x 2 2 of discriminant − 47 are given. Moreover, a basis for the space S 4 ( Γ 0 ( 47 ) , 1 ) are constructed, and the formulas for r ( n ; F 4 ) , r ( n ; G 4 ) , r ( n ; F 3 ⊕ G 1 ) , r ( n ; F 2 ⊕ G 2 ) , and r ( n ; F 1 ⊕ G 3 ) are derived.