Application of Modular Equations to some Quadratic Forms

After the discovery by Jacobi of the identity which gives the number of representations of a number as a sum of four squares, interest naturally arose in the more general problem of finding the number of ways in which a number can be expressed in the form ax₁² + bx₂²+ cx₃² + dx₄², where a, b, c, d are given positive integers and xx, x2, xs, xt are integral variables.