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NEWFORMS OF LEVEL 4 AND OF TRIVIAL CHARACTER
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 Title & Authors
NEWFORMS OF LEVEL 4 AND OF TRIVIAL CHARACTER
Zhang, Yichao;
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 Abstract
In this paper, we consider characters of 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.
 Keywords
Fricke involution;non-Dirichlet character;
 Language
English
 Cited by
 References
1.
A. O. L. Atkin and J. Lehner, Hecke operators on $\Gamma_{0}(m)$, Math. Ann. 185 (1970), no. 2, 134-160. crossref(new window)

2.
R. E. Borcherds, Automorphic forms with singularities on Grassmannians, Invent. Math. 132 (1998), no. 3, 491-562. crossref(new window)

3.
J. H. Bruinier and M. Bundschuh, On Borcherds products associated with lattices of prime discriminant, Ramanujan J. 7 (2003), no. 1-3, 49-61. crossref(new window)

4.
Keith Conrad, $SL_2(\mathbb{Z})$, http://www.math.uconn.edu/-kconrad/blurbs/grouptheory/SL(2, Z).pdf.

5.
W.-C. W. Li, Newforms and functional equations, Math. Ann. 212 (1975), no. 4, 285-315. crossref(new window)

6.
T. Miyake, Modular Forms, Springer Verlag, 2006.

7.
Y. Yang, Newforms of level 4N, Unpublished, 2010.

8.
D. Zagier, Elliptic modular forms and their applications, The 1-2-3 of modular forms, 1-103, Uiversitext, Springer, 2008.

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.