# CUSP FORMS IN S4 (Γ0 (79)) AND THE NUMBER OF REPRESENTATIONS OF POSITIVE INTEGERS BY SOME DIRECT SUM OF BINARY QUADRATIC FORMS WITH DISCRIMINANT -79

• Kendirli, Baris
• Published : 2012.05.31
• 52 6

#### Abstract

A basis of a subspace of $S_4({\Gamma}_0(79))$ is given and the formulas for the number of representations of positive integers by some direct sums of the quadratic forms $x^2_1+x_1x_2+20x^2_2$, $4x^2_1{\pm}x_1x_2+5x^2_2$, $2x^2_1{\pm}x_1x_2+10x^2_2$ are determined.

#### Keywords

cusp forms;representation number;theta series

#### References

1. H. Ivaniec and E. Kowalski, Analytic Number Theory, American Mathematical Society Colloquium publications volume 53, 2000.
2. G. Lomadze, On the number of representations of positive integers by a direct sum of binary quadratic forms with discriminant -23, Georgian Math. J. 4 (1997), no. 6, 523-532. https://doi.org/10.1023/A:1022103424996
3. T. Miyake, Modular Forms, Springer-Verlag, 1989.

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3. Fourier Coefficients of a Class of Eta Quotients of Weight 16 with Level 12 vol.06, pp.08, 2015, https://doi.org/10.4236/am.2015.68133
4. Cusp forms in S 6(Γ 0(23)), S 8(Γ 0(23)) and the number of representations of numbers by some quadratic forms in 12 and 16 variables vol.34, pp.2, 2014, https://doi.org/10.1007/s11139-013-9480-4