Eta-quotients and elliptic curves

Authors:
Yves Martin and Ken Ono

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3169-3176

MSC (1991):
Primary 11F20, 11GXX

DOI:
https://doi.org/10.1090/S0002-9939-97-03928-2

MathSciNet review:
1401749

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we list all the weight newforms that are products and quotients of the Dedekind eta-function

where There are twelve such and we give a model for the strong Weil curve whose Hasse-Weil function is the Mellin transform for each of them. Five of the have complex multiplication, and we give elementary formulae for their Fourier coefficients which are sums of Hecke Grössencharacter values. These formulae follow easily from well known series infinite product identities.

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Additional Information

**Yves Martin**

Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720

Email:
ymartin@math.berkeley.edu

**Ken Ono**

Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540;
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

Email:
ono@math.ias.edu, ono@math.psu.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03928-2

Keywords:
Eta-quotient,
elliptic curves

Received by editor(s):
March 2, 1996

Received by editor(s) in revised form:
May 17, 1996

Additional Notes:
The second author is supported by NSF grants DMS-9508976 and DMS-9304580.

Communicated by:
William W. Adams

Article copyright:
© Copyright 1997
American Mathematical Society