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

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 0(48) with character.

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