Theta products and eta quotients of level 24 and weight 2
Aygin, Zafer Selcuk
Date of Issue2017
School of Physical and Mathematical Sciences
We find bases for the spaces M2(Γ0(24),(d⋅))M2(Γ0(24),(d⋅)) (d=1,8,12,24d=1,8,12,24) of modular forms. We determine the Fourier coefficients of all 3535 theta products φ[a1,a2,a3,a4](z)φ[a1,a2,a3,a4](z) in these spaces. We then deduce formulas for the number of representations of a positive integer nn by diagonal quaternary quadratic forms with coefficients 11, 22, 33 or 66 in a uniform manner, of which 1414 are Ramanujan's universal quaternary quadratic forms. We also find all the eta quotients in the Eisenstein spaces E2(Γ0(24),(d⋅))E2(Γ0(24),(d⋅)) (d=1,8,12,24d=1,8,12,24) and give their Fourier coefficients.
Dedekind eta function
Functiones et Approximatio, Commentarii Mathematici
© 2017 Adam Mickiewicz University, Faculty of Mathematics and Computer Science. This is the author created version of a work that has been peer reviewed and accepted for publication in Functiones et Approximatio, Commentarii Mathematici, by Adam Mickiewicz University, Faculty of Mathematics and Computer Science. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.7169/facm/1628].