Every elliptic modular form of integral weight greater than 1 lies in products of at most two cusp expansions of Eisenstein series; for weights above 2, exactly two suffice.
A positive proportion of elliptic curves over Q have rank one
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All modular forms of weight 2 can be expressed by Eisenstein series
Every elliptic modular form of integral weight greater than 1 lies in products of at most two cusp expansions of Eisenstein series; for weights above 2, exactly two suffice.