We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.
@article{bwmeta1.element.doi-10_1515_math-2015-0062,
author = {SoYoung Choi and Chang Heon Kim},
title = {
Linear relations between modular forms for G
0
+
(p)
},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {06478638},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0062}
}
SoYoung Choi; Chang Heon Kim.
Linear relations between modular forms for Г
0
+
(p)
. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0062/
[1] A. O. L. Atkin and J. Lehner, Hecke operators on Г0(m), Math. Ann. 185 (1970), 134-160. | Zbl 0177.34901
[2] R. E. Borcherds, Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109 (1992), 405–444. | Zbl 0799.17014
[3] D. Choi amd Y. Choie, p -adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight, Israel J. Math. 175 (2010), 61–83. | Zbl 1239.11054
[4] D. Choi amd Y. Choie, Weight-dependent congruence properties of modular forms, J. Number Theory 122 (2007), no. 2, 301–313. [WoS] | Zbl 1158.11020
[5] D. Choi amd Y. Choie, Linear relations among the Fourier coefficients of modular forms on groups Г0(N) of genus zero and their applications, J. Math. Anal. Appl. 326 (2007), no. 1, 655–666. [WoS] | Zbl 1114.11042
[6] S. Choi and C. H. Kim, Congruences for Hecke eigenvalues in higher level cases, J. Number Theory 131 (2011), no. 11, 2023– 2036. [WoS] | Zbl 1263.11055
[7] S. Choi and C. H. Kim, Basis for the space of weakly holomorphic modular forms in higher level cases, J. Number Theory 133 (2013), no. 4, 1300–1311. [WoS] | Zbl 1282.11027
[8] Y. Choie, W. Kohnen and K Ono, Linear relations between modular form coefficients and non-ordinary primes, Bull. London Math. Soc. 37 (2005), no. 3, 335–341. | Zbl 1155.11325
[9] J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. London Math. Soc. 11 (1979), 308–339.
[10] W. Duke and P. Jenkins, On the zeros and coefficients of certain weakly holomorphic modular forms, Pure Appl. Math. Q. 4 (2008), 1327–1340. | Zbl 1200.11027
[11] P. Guerzhoy, Hecke operators for weakly holomorphic modular forms and supersingular congruences, Proc. Amer. Math. Soc. 136 (2008), 3051-3059. [WoS] | Zbl 1173.11028
[12] K. Harada, Moonshine of finite groups, The Ohio State University Lecture Notes.
[13] N. Koblitz, Introduction to elliptic curves and modular forms, Springer-Verlag, New York, 1984. | Zbl 0553.10019
[14] M. Koike, On replication formula and Hecke operators, Nogoya University, preprint.
[15] A. Krieg, Modular forms on the Fricke group, Abh. Math. Sem. Univ. Hamburg 65 (1995), 293-299. | Zbl 0851.11027
[16] S. Lang, Introduction to modular forms, Grundlehren der mathematischen Wissenschaften, No. 222. Springer-Verlag, Berlin-New York, 1976.
[17] J. Lewis and D. Zagier, Periodic functions for Maass wave forms I, Ann. of Math. (2) 153 (2001), 191-258. | Zbl 1061.11021
[18] T. Miyake, Modular forms, Springer, 1989.
[19] K. Ono, The web of modularity: Arithmetic of the coefficients of modular forms and q-series, volume 102 of CBMS regional conference series in mathematics. American Mathematical Society, 2004.
[20] J. Shigezumi, On the zeros of the Eisenstein series for Г0(5) and Г0(7), Kyushu J. Math. 61 (2007), no. 2, 527-549. | Zbl 1147.11023
[21] G. Shimura, Introduction to the arithmetic theory of automorphic forms, Princeton University Press, 1971. | Zbl 0221.10029
[22] W. Stein, http://wstein.org.
[23] D. Zagier, Introduction to modular forms, From number theory to physics (Les Houches, 1989), 238-291, Springer, 1992. | Zbl 0791.11022