On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6

Published 13 Jul 2016 in math.NT | (1607.03809v3)

Abstract: In this paper, we find formulas for the number of representations of certain diagonal octonary quadratic forms with coefficients $1,2,3,4$ and $6$. We obtain these formulas by constructing explicit bases of the space of modular forms of weight $4$ on $\Gamma_0(48)$ with character.

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