Properties

 Label 3479.1 Level 3479 Weight 1 Dimension 256 Nonzero newspaces 11 Newform subspaces 23 Sturm bound 987840 Trace bound 9

Defining parameters

 Level: $$N$$ = $$3479 = 7^{2} \cdot 71$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$11$$ Newform subspaces: $$23$$ Sturm bound: $$987840$$ Trace bound: $$9$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3479))$$.

Total New Old
Modular forms 4541 3603 938
Cusp forms 341 256 85
Eisenstein series 4200 3347 853

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 248 8 0 0

Trace form

 $$256 q + 5 q^{2} - q^{3} + q^{4} + 3 q^{5} + 6 q^{6} - 38 q^{8} - q^{9} + O(q^{10})$$ $$256 q + 5 q^{2} - q^{3} + q^{4} + 3 q^{5} + 6 q^{6} - 38 q^{8} - q^{9} + 4 q^{10} + 2 q^{11} + 3 q^{12} - 18 q^{15} + 2 q^{16} - 2 q^{18} - q^{19} - 4 q^{20} - 8 q^{22} + 2 q^{23} - q^{24} - q^{25} - 2 q^{27} - 3 q^{29} - 5 q^{30} + 9 q^{32} + 61 q^{36} + 5 q^{37} - 7 q^{38} + 2 q^{40} - 15 q^{43} + 6 q^{44} + 3 q^{45} + 4 q^{46} - 6 q^{48} - 13 q^{50} + 2 q^{53} + 6 q^{54} - 2 q^{57} + 6 q^{58} - q^{60} + 36 q^{64} + 2 q^{67} - 11 q^{71} + 3 q^{72} + 3 q^{73} + q^{74} - 4 q^{75} + 3 q^{76} + q^{79} - 4 q^{80} - 2 q^{81} + q^{83} + 6 q^{86} - 5 q^{87} - 27 q^{88} - q^{89} - q^{90} - 12 q^{92} - q^{96} - 4 q^{99} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3479))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
3479.1.c $$\chi_{3479}(2841, \cdot)$$ None 0 1
3479.1.d $$\chi_{3479}(638, \cdot)$$ 3479.1.d.a 1 1
3479.1.d.b 2
3479.1.d.c 2
3479.1.d.d 2
3479.1.d.e 3
3479.1.d.f 6
3479.1.d.g 12
3479.1.g $$\chi_{3479}(851, \cdot)$$ 3479.1.g.a 2 2
3479.1.g.b 4
3479.1.g.c 4
3479.1.g.d 6
3479.1.g.e 6
3479.1.g.f 12
3479.1.g.g 24
3479.1.h $$\chi_{3479}(2273, \cdot)$$ None 0 2
3479.1.r $$\chi_{3479}(1079, \cdot)$$ 3479.1.r.a 4 4
3479.1.s $$\chi_{3479}(1567, \cdot)$$ None 0 4
3479.1.u $$\chi_{3479}(258, \cdot)$$ None 0 6
3479.1.w $$\chi_{3479}(176, \cdot)$$ None 0 6
3479.1.x $$\chi_{3479}(141, \cdot)$$ None 0 6
3479.1.y $$\chi_{3479}(239, \cdot)$$ None 0 6
3479.1.z $$\chi_{3479}(680, \cdot)$$ None 0 6
3479.1.ba $$\chi_{3479}(449, \cdot)$$ None 0 6
3479.1.bb $$\chi_{3479}(736, \cdot)$$ 3479.1.bb.a 6 6
3479.1.bc $$\chi_{3479}(48, \cdot)$$ None 0 6
3479.1.be $$\chi_{3479}(314, \cdot)$$ None 0 6
3479.1.bg $$\chi_{3479}(20, \cdot)$$ None 0 6
3479.1.bj $$\chi_{3479}(517, \cdot)$$ None 0 6
3479.1.bk $$\chi_{3479}(356, \cdot)$$ None 0 6
3479.1.bn $$\chi_{3479}(1511, \cdot)$$ None 0 6
3479.1.bo $$\chi_{3479}(974, \cdot)$$ None 0 6
3479.1.bp $$\chi_{3479}(820, \cdot)$$ None 0 6
3479.1.bq $$\chi_{3479}(545, \cdot)$$ None 0 6
3479.1.cc $$\chi_{3479}(999, \cdot)$$ 3479.1.cc.a 8 8
3479.1.cd $$\chi_{3479}(1292, \cdot)$$ 3479.1.cd.a 8 8
3479.1.cn $$\chi_{3479}(250, \cdot)$$ None 0 12
3479.1.co $$\chi_{3479}(389, \cdot)$$ None 0 12
3479.1.cp $$\chi_{3479}(254, \cdot)$$ None 0 12
3479.1.cr $$\chi_{3479}(45, \cdot)$$ None 0 12
3479.1.cs $$\chi_{3479}(187, \cdot)$$ None 0 12
3479.1.cv $$\chi_{3479}(143, \cdot)$$ None 0 12
3479.1.cw $$\chi_{3479}(101, \cdot)$$ None 0 12
3479.1.cz $$\chi_{3479}(332, \cdot)$$ None 0 12
3479.1.db $$\chi_{3479}(1097, \cdot)$$ 3479.1.db.a 12 12
3479.1.dc $$\chi_{3479}(165, \cdot)$$ 3479.1.dc.a 12 12
3479.1.dd $$\chi_{3479}(744, \cdot)$$ None 0 12
3479.1.de $$\chi_{3479}(247, \cdot)$$ None 0 12
3479.1.df $$\chi_{3479}(212, \cdot)$$ None 0 12
3479.1.dg $$\chi_{3479}(23, \cdot)$$ None 0 12
3479.1.dh $$\chi_{3479}(51, \cdot)$$ None 0 12
3479.1.dj $$\chi_{3479}(103, \cdot)$$ None 0 12
3479.1.dl $$\chi_{3479}(160, \cdot)$$ None 0 24
3479.1.dm $$\chi_{3479}(113, \cdot)$$ None 0 24
3479.1.dn $$\chi_{3479}(78, \cdot)$$ None 0 24
3479.1.do $$\chi_{3479}(27, \cdot)$$ None 0 24
3479.1.dr $$\chi_{3479}(76, \cdot)$$ None 0 24
3479.1.ds $$\chi_{3479}(202, \cdot)$$ None 0 24
3479.1.dv $$\chi_{3479}(6, \cdot)$$ None 0 24
3479.1.dx $$\chi_{3479}(363, \cdot)$$ None 0 24
3479.1.dz $$\chi_{3479}(146, \cdot)$$ None 0 24
3479.1.ea $$\chi_{3479}(99, \cdot)$$ 3479.1.ea.a 24 24
3479.1.eb $$\chi_{3479}(92, \cdot)$$ None 0 24
3479.1.ec $$\chi_{3479}(22, \cdot)$$ None 0 24
3479.1.ed $$\chi_{3479}(155, \cdot)$$ None 0 24
3479.1.ee $$\chi_{3479}(85, \cdot)$$ None 0 24
3479.1.ef $$\chi_{3479}(134, \cdot)$$ None 0 24
3479.1.eh $$\chi_{3479}(90, \cdot)$$ None 0 24
3479.1.eq $$\chi_{3479}(40, \cdot)$$ None 0 48
3479.1.es $$\chi_{3479}(44, \cdot)$$ None 0 48
3479.1.et $$\chi_{3479}(207, \cdot)$$ None 0 48
3479.1.eu $$\chi_{3479}(46, \cdot)$$ None 0 48
3479.1.ev $$\chi_{3479}(305, \cdot)$$ None 0 48
3479.1.ew $$\chi_{3479}(53, \cdot)$$ None 0 48
3479.1.ex $$\chi_{3479}(67, \cdot)$$ 3479.1.ex.a 48 48
3479.1.ey $$\chi_{3479}(19, \cdot)$$ 3479.1.ey.a 48 48
3479.1.fa $$\chi_{3479}(38, \cdot)$$ None 0 48
3479.1.fd $$\chi_{3479}(75, \cdot)$$ None 0 48
3479.1.fe $$\chi_{3479}(5, \cdot)$$ None 0 48
3479.1.fh $$\chi_{3479}(3, \cdot)$$ None 0 48
3479.1.fi $$\chi_{3479}(10, \cdot)$$ None 0 48
3479.1.fk $$\chi_{3479}(11, \cdot)$$ None 0 48
3479.1.fl $$\chi_{3479}(102, \cdot)$$ None 0 48
3479.1.fm $$\chi_{3479}(12, \cdot)$$ None 0 48

Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3479))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3479)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(71))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(497))$$$$^{\oplus 2}$$