Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All modular forms of weight 2 can be expressed by Eisenstein series   We show that every elliptic modular form of integral weight greater than $1$
can be expressed as linear combinations of products of at most two cusp
expansions of Eisenstein series. This removes the obstruction of nonvanishing
central $\mathrm{L}$-values present in all previous work. For weights greater
than $2$, we refine our result further, showing that linear combinations of
products of exactly two cusp expansions of Eisenstein series suffice.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg