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I only find Cohen–Eisenstein series of weight 3/2 (in the paper A note on the Fourier coefficients of a Cohen-Eisenstein series). I founded some general definition in "Modular Forms with Integral and Half-Integral Weights by Dingyi Pei and Xueli Wang" section 7.4. But I am not able to relate to the description in the paper.

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    $\begingroup$ As things stand, this does not seem like a suitable question for MO. Where did you see the definition? Where did you see a reference, without definition, to the general case? $\endgroup$
    – LSpice
    Jul 22, 2019 at 4:02
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    $\begingroup$ I found the definition in the following paper arxiv.org/abs/1504.03971 $\endgroup$
    – SUNIL PASUPULATI
    Jul 22, 2019 at 4:19
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    $\begingroup$ I found several hits when searching for "Cohen Eisenstein series" in google (eg section 3 of this: kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1274-22.pdf), though it's not clear how the definitions relate to the one in the paper you give. $\endgroup$
    – David Roberts ♦
    Jul 22, 2019 at 5:31
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    $\begingroup$ I founded some general definition in "Modular Forms with Integral and Half-Integral Weights by Dingyi Pei and Xueli Wang" section 7.4 I am not able to relate to the description in the paper. $\endgroup$
    – SUNIL PASUPULATI
    Jul 22, 2019 at 10:14
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    $\begingroup$ Have you looked at Cohen's paper (Math Ann 1975)? Even with the edit, I don't really understand what this question is asking. $\endgroup$
    – Kimball
    Jul 23, 2019 at 0:44

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