Representations by sextenary quadratic forms with coefficients 1,2,3 and 6 and on newforms in S3(Γ0(24),χ)

We use the theory of modular forms to give formulas for the number of representations of n by all sextenary quadratic forms with coefficients 1,2,3,6. We also apply our results to write newforms in S3(Γ0(24),χ) in terms of eta quotients.