Fourier Coefficients of A Class of Eta Quotients of Weight 6

Abstract

Recently,Williams expressed all coefficients of one hundred and twenty-six eta quotients in terms of σ(n), σ(n/2), σ(n/3) and σ(n/6), and Yao, Xia and Jin, expressed only even coefficients of one hundred and four eta quotients in terms of σ3(n), σ3(n/2), σ3(n/3) and σ3(n/6). The Fourier series expansions of a class of eta quotients in terms of σk-1(n), σk-1(n/2), σk-1(n/3) and σk-1(n/6) for k = 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 have been expressed by the author. The Fourier series expansions of a class of eta quotients in M2 (Γ0, χ) in terms of σ(n), σ(n/2), σ(n/3) and σ(n/6) has been found by Alaca and the Fourier series expansions of a class of eta quotients in M4 (Γ0, χ) in terms of σ3(n), σ3(n/2), σ3(n/3) and σ3(n/6) has been determined by the author. Here, we will determine the coefficients of the Fourier series expansions of a class of eta quotients in M6 (Γ0, χ) in terms of σ5(n), σ5(n/2), σ5(n/3), σ5(n/6) and Fourier coefficients of the eight eta quotients.