# Period polynomials and explicit formulas for Hecke operators on Γ 0 (2)

@inproceedings{Fukuhara2009PeriodPA, title={Period polynomials and explicit formulas for Hecke operators on Γ 0 (2)}, author={Shinji Fukuhara and Yifan Yang}, year={2009} }

Let Sw+2( 0(N)) be the vector space of cusp forms of weight w+2 on the congruence subgroup 0(N). We first determine explicit formulas for period polynomials of elements in Sw+2( 0(N)) by means of Bernoulli polynomials. When N = 2, from these explicit formulas we obtain new bases for Sw+2( 0(2)), and extend the Eichler-Shimura-Manin isomorphism theorem to 0(2). This implies that there are natural correspondences between the spaces of cusp forms on 0(2) and the spaces of period polynomials. Based… CONTINUE READING

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