In this paper, we find the number of representations of the quadratic form, for k = 7, 9, 11, 12, 14 using the theory of modular forms. By comparing our formulas with the formulas obtained by G. A. Lomadze, we obtain the Fourier coefficients of certain newforms of level 3 and weights 7, 9, 11 in terms of certain finite sums involving the solutions of similar quadratic forms of lower variables. In the case of 24 variables, comparison of these formulas gives rise to a new formula for the Ramanujan tau function.