N. Kachakhidze

On the Representation of Numbers by the Direct Sums of Some Quaternary Quadratic Forms

The systems of bases are constructed for the spaces of cusp forms $S_{2m}(\Gm_0(5),\chi^m)$ and $S_{2m}(\Gm_0(13),\chi^m)$ for an arbitrary integer $m\geq 2$. Formulas are obtained for the number of representations of a positive integers by the direct sums of some quaternary quadratic forms