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 S4(Γ0(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 x12 + x1 x2 + 48x2, 2x12 + x1 x2 + 24x2, 3x12 + x1 x2 + 16x2, 4x12 + x1 x2 + 12x2, 5x12 + 3x1 x2 + 10x2, 6x12 + x1 x2 + 8x2, 6x12 + 5x1 x2 + 9x2 of the class group of equivalence classes of quadratic forms with discriminant −191.