Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eisenstein series identities based on partial fraction decomposition   From the theory of modular forms, there are exactly $[(k-2)/6]$ linear
relations among the Eisenstein series $E_k$ and its products $E_{2i}E_{k-2i}\
(2\le i \le [k/4])$. We present explicit formulas among these modular forms
based on the partial fraction decomposition, and use them to determining a
basis of the space of modular forms of weight $k$ on ${\rm SL}_2({\mathbb Z})$.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc