Representations by sexternary quadratic forms with coefficients 1,2,5 and 10

In this article, we find bases for the spaces of modular forms $M_3({\mathrm{\Gamma }}_0(40),\left(\frac{d}{\cdot }\right))$ for $d=-4,-8,-20\text{ and }-40.$ We then derive formulas for the number of representations of a positive integer by all the diagonal sextenary quadratic forms with coefficients $$ and $10$.