On the number of representation of integers by the direct sum of BQFs with discriminant −191

Abstract

In this study we find a basis of the space $S_4(Gamma_0$(191)) and derive explicit formulae for the number of representation of positive integers by all possible direct sum of 13 quadratic forms from the representatives $x^2_1 + x_1 x_2 + 48x^2_2 , 2x^2_1 + x_1x_2 + 24x^2_2 , 3x^2_1 + x_1 x_2 + 16x^2_2 , 4x^2_1 + x_1 x_2 + 12x^2_2 , 5x^2_ 1 + 3x_1 x_2 +10x^2_2 , 6x^2_1 + x_1 x_2 +8x^2_2 , 6x^2_1 +5x_1 x_2 +9x^2_2$ of the class group of equivalence classes of quadratic forms with discriminant −191.