Fourier series of a class of eta quotients (Q2890252)

This research comprises 126 eta quotients of the form \(\prod_{d\mid 12} \eta^{a(d)}(dz)\) with exponents \(a(d)\in\mathbb Z\) which are holomorphic non-cuspidal modular forms of level 12 and weight \({1\over 2} \sum_d a(d)= 2\), and where \(\sum_d da(d)\) is a multiple of 24. (A few of them are derived from eta quotients whose levels are proper divisors of 12.) The author gives an explicit formula which expresses in a unified way the Fourier coefficients \(c(n)\) of each of his eta quotients as a linear combination of divisor sums \(\sigma\left({n\over d}\right)\) with \(d\mid 12\). Equivalently, the eta quotients are written as linear combinations of Eisenstein series \(E_2(dz)\), \(d\mid 12\), of weight \(2\). -- There is almost no overlap of results with the reviewer's [Eta products and theta series identities. Berlin: Springer (2011; Zbl 1222.11060)], since level 12 and weight, 2 was not treated in this monograph.