International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 12, Pages 637-646
doi:10.1155/S0161171204203076

On the number of representations of positive integers by quadratic forms as the basis of the space S4(Γ0(47),1)

Ahmet Tekcan and Osman Bızım

Department of Mathematics, Faculty of Science, University of Uludag, Görükle, Bursa 16059, Turkey

Received 11 March 2002

Copyright © 2004 Ahmet Tekcan and Osman Bızım. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The number of representations of positive integers by quadratic forms F1=x12+x1x2+12x22 and G1=3x12+x1x2+4x22 of discriminant 47 are given. Moreover, a basis for the space S4(Γ0(47),1) are constructed, and the formulas for r(n;F4), r(n;G4), r(n;F3G1), r(n;F2G2), and r(n;F1G3) are derived.