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NEWFORMS OF LEVEL 4 AND OF TRIVIAL CHARACTER

Yichao Zhang
대한수학회 (The Korean Mathematical Society)|2014.10|대한수학회논문집 (Communications of the KMS)|제29권 제4호|pp. 497-503

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참고문헌

키워드

Fricke involutionnon-Dirichlet character
주제분류수학

초록

In this paper, we consider characters of SL2(Z) and then apply them to newforms of integral weight, level 4 and of trivial character. More precisely, we prove that all of them are actually level 1 forms of some nontrivial character. As a byproduct, we prove that they all are eigenfunctions of the Fricke involution with eigenvalue −1.

Abstract

In this paper, we consider characters of SL2(Z) and then apply them to newforms of integral weight, level 4 and of trivial character. More precisely, we prove that all of them are actually level 1 forms of some nontrivial character. As a byproduct, we prove that they all are eigenfunctions of the Fricke involution with eigenvalue −1.

참고문헌 (10)

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  2. R. E. Borcherds, "Automorphic forms with singularities on Grassmannians", Invent. Math, 132(3), pp.491~562 (1998)
  3. J. H. Bruinier, "On Borcherds products associated with lattices of prime discriminant", Ramanujan J, 7(1-3), pp.49~61 (2003)
  4. "SL2(Z)"[URL]
  5. W.-C, "Newforms and functional equations", Math. Ann, 212(4), pp.285~315 (1975)
  6. T. Miyake, "Modular Forms" (2006), Springer Verlag
  7. Y. Yang, "Newforms of level 4N", Unpublished, ~ (2010)
  8. D. Zagier, "The 1-2-3 of modular forms", pp.1~103 (2008), Springer
  9. Y. Zhang, "Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms", preprint, arXiv: 1308.1037, ~ (2013)
  10. Y. Zhang, "An isomorphism between scalar-valued modular forms and modular forms for Weil representations", preprint, arXiv:1307.4390, ~ (2014)

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