Representations by sextenary quadratic forms with coefficients $1,2,3$ and $6$ and on newforms in $S_{3} (\Gamma_0 (24), \chi )$

Zafer Selcuk Aygin

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arXiv · 1705.01244

Representations by sextenary quadratic forms with coefficients $1,2,3$ and $6$ and on newforms in $S_{3} (\Gamma_0 (24), \chi )$

Zafer Selcuk Aygin

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Abstract

We use theory of modular forms to give formulas for $N(1^{l_1},2^{l_2},3^{l_3},6^{l_6};n)$ for all $l_1,l_2,l_3,l_6 \in \mathbb{N}_0$, with $l_1+l_2+l_3+l_6=6$. We also apply our results to write newforms in $S_{3} (\Gamma_0 (24), \chi )$ in terms of eta quotients.

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Zafer Selcuk Aygin. 2017-05-03. Representations by sextenary quadratic forms with coefficients $1,2,3$ and $6$ and on newforms in $S_{3} (\Gamma_0 (24), \chi )$. https://arxiv.org/abs/1705.01244

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