On a Space of Some Theta Functions

Yoshiyuki Kitaoka
1971 Nagoya mathematical journal  
In the theory of modular forms there is an interesting problem whether every modular form can be expressed as a linear comination of theta functions. For this Eichler proved in [1] that for a sufficiently large prime q all modular forms of degree — 2m(m = 1,2, · · ·) for Γ0(q) can be represented by linear combinations of theta functios of degree — 2m with level 1 and q. We prove this theorem for q = 2, 3, 5 and 11 by using a theorem of Siegel for q = 2, 3, 5 and a general result of Eichler for
more » ... ult of Eichler for q = 11. The former method is shown in Schoeneberg [2].
doi:10.1017/s0027763000014264 fatcat:cedtkv7gjvfxfc7o5p7mdkwq3i