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 ${\Gamma }_0(48)$ with character.

43 pages, 10 Tables, accepted for publication in IJNT

References in corpus (1)

• On Eisenstein series in $M_{2k}({\Gamma }_0(N))$ and their applications

Cited by in corpus (2)

• On the representations of a positive integer by certain classes of quadratic forms in eight variables
• Representations of an integer by some quaternary and octonary quadratic forms