Abstract
We show that every modular form onΓ0(2n) (n⩾ 2) can be expressed as a sum of eta-quotients, which is a partial answer to Ono's problem. Furthermore, we construct a primitive generator of the ring class field of the order of conductor 4N(N⩾ 1) in an imaginary quadratic field in terms of the special value of a certain eta-quotient.
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