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On Monomial Relations Between Eisenstein Series
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We show that the relations E8 = E24, E10 =E4E6, and E14 = E6 E8 are the only relations of the form Ek = El Ek-l , where Ek is the Eisen-stein series of weight k for the full modular group. More generally we show that, apart from fifteen exceptions, the product of two level one eigenforms is never an eigenform. The proof uses the Rankin-Selberg method.
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