We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on Γ₀(N) multiplied by their twisted period polynomials in terms of the product of those twisted Kronecker series, when N is square free. This extends an identity of Zagier among period polynomials, Hecke eigenforms and a quotient of Jacobi theta series.
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Blakestad et al. (2024) studied this question.
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