Theta products and eta quotients of level 24 and weight 2
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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/84889 http://hdl.handle.net/10220/43604 |
| Summary: | 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. |
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