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Integral traces of weak Maass forms of genus zero odd prime level

Abstract

Duke and the second author defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half-integral weight and level 4 and showed that these lifts preserve the integrality of Fourier coefficients. We show that the generalization of these lifts to modular forms of genus 0 odd prime level also preserves the integrality of Fourier coefficients.

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Correspondence to Paul Jenkins.

Additional information

This work was partially supported by a grant from the Simons Foundation (#281876 to Paul Jenkins).

Appendix

Appendix

Here we list the beginning of the Fourier expansions of the form with the highest leading exponent in each of the bases described in Sect. 3 (Tables 1, 2, 3, and 4).

Table 1 List of bases for \(M^+_{k}(12)\)
Table 2 List of bases for \(M^+_{k}(20)\)
Table 3 List of bases for \(M^+_{k}(28)\)
Table 4 List of bases for \(M^+_{k}(52)\)

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Green, N., Jenkins, P. Integral traces of weak Maass forms of genus zero odd prime level. Ramanujan J 42, 453–478 (2017). https://doi.org/10.1007/s11139-015-9769-6

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  • DOI: https://doi.org/10.1007/s11139-015-9769-6

Keywords

  • Zagier lift
  • Weakly holomorphic modular forms
  • Kohnen plus space

Mathematics Subject Classification

  • 11F11
  • 11F30