arXiv subjects
Publications and source records attributed to Suda Tomohiko.
We study modular forms of some congruence subgroups. In this paper, we treat the cases level is 2-power, 3-power or 5. Structures of graded rings and many identities of infinite sum or infinite product are given. Theory of rational (1/3, 1/4, 1/5 etc) weight or more formally weight modular form are introduced.
We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.
In this paper, for a square-free integer l>1, a even positive integer k and a positive integer N, we give a trace formula of the Hecke operator T(l) on the space S_k^0(N) of all newforms of weight k and level Γ_0(N). Moreover, we give a decomposition S_k^0(N)=\oplus_{i|N}S_k^0(N;i) and also give a trace formula of T(l) on S_k^0(N;i).
The sets of primitive foms may be decomposed into some Galois conjugacy classes. The purpose of this paper is to write down all of such classes with cardinal 1 or 2, explicitly in terms of some Eisenstein series, for level 1,2,3,4,6,8,9. For level 6, some calculations have not yet been completed.
In this paper, we study the explicit structure of the graded ring of elliptic modular forms for the congruence subgroup $Γ_0(N)$ with N=1,2,3,4,5,6,7,8,9,10,12,16,18,25. More precisely, making use of some relations between Fourier expansions, we determine the ring by a quotient of the polynomial ring in several variables.