Theta products and eta quotients of level 24 and weight 2

• Main Authors: Alaca, Ayşe, Alaca, Şaban, Aygin, Zafer Selcuk
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2017
• Subjects: Eta quotients; Dedekind eta function
• Online Access: https://hdl.handle.net/10356/84889; http://hdl.handle.net/10220/43604
• Institution: Nanyang Technological University

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.