We study the linear relations among the Fourier coefficients of modular forms on the group Γ0 (N) of genus zero. Applying these linear relations, congruence properties of Hecke eigenforms, replicable properties of Hauptmoduln and congruences of representation numbers of the sums of n squares can be obtained. The eta-quotient expression of the unique normalized modular form ΔN (z) of weight 12 on Γ0 (N) with a zero of maximum order at ∞ is listed.
|Number of pages||12|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2007 Feb 1|
- Modular forms
ASJC Scopus subject areas
- Applied Mathematics