Fourier Coefficients of a Class of Eta Quotients of Weight 12 with Level 12

Abstract

Recently, Williams and then Yao, Xia and Jin discovered explicit formulas for the coefficients of the Fourier series expansions of a class of eta quotients. Williams expressed all coefficients of 126 eta quotients in terms of ?(n),?((n/2)),?((n/3)) and ?((n/6)) and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of 104 eta quotients in terms of ??(n),??((n/2)),??((n/3)) and ??((n/6)).Here, we will

express the even Fourier coefficients of 2 eta quotients i.e., the Fourier coefficients of the sum, f(q)+f(-q), of 2 eta quotients in terms of ??(n),??((n/2)),??((n/3)),??((n/4)),??((n/6)),??((n/(12))),???(n),???((n/2)),
???((n/3)),???((n/4)),???((n/6)),???((n/(12))),?(n)(tau function),?((n/2)),?((n/3)),?((n/4)),?((n/6)),?((n/(12)))
and the odd Fourier coefficients of 393 eta quotients in terms of ??(n),??((n/2)),??((n/3)),??((n/4)),??((n/6)),??((n/(12))),???(n),???((n/2)),
???((n/3)),???((n/4)),???((n/6)),???((n/(12))),?(n),?((n/2)),?((n/3)),?((n/4)),?((n/6)),?((n/(12))) and f??,?,f??.