# Properties

 Label 1470.2 Level 1470 Weight 2 Dimension 12416 Nonzero newspaces 24 Sturm bound 225792 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$225792$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1470))$$.

Total New Old
Modular forms 58368 12416 45952
Cusp forms 54529 12416 42113
Eisenstein series 3839 0 3839

## Trace form

 $$12416q - 10q^{3} - 16q^{4} - 28q^{5} - 26q^{6} - 32q^{7} - 32q^{9} + O(q^{10})$$ $$12416q - 10q^{3} - 16q^{4} - 28q^{5} - 26q^{6} - 32q^{7} - 32q^{9} - 20q^{10} - 80q^{11} - 2q^{12} - 48q^{13} + 10q^{15} - 24q^{17} + 56q^{18} - 48q^{19} + 4q^{20} + 20q^{21} + 8q^{22} - 24q^{23} + 22q^{24} + 40q^{25} + 48q^{26} + 134q^{27} + 24q^{28} + 120q^{29} + 106q^{30} + 48q^{31} + 152q^{33} + 112q^{34} + 96q^{35} + 64q^{36} + 352q^{37} + 240q^{38} + 352q^{39} + 72q^{40} + 376q^{41} + 180q^{42} + 272q^{43} + 176q^{44} + 200q^{45} + 456q^{46} + 336q^{47} + 26q^{48} + 576q^{49} + 80q^{50} + 396q^{51} + 104q^{52} + 240q^{53} + 70q^{54} + 460q^{55} + 144q^{56} + 152q^{57} + 400q^{58} + 376q^{59} + 60q^{60} + 552q^{61} + 96q^{62} + 84q^{63} - 16q^{64} + 120q^{65} + 24q^{66} + 336q^{67} - 24q^{68} + 112q^{69} - 56q^{72} + 232q^{73} - 104q^{74} + 158q^{75} - 32q^{76} - 72q^{77} - 84q^{78} - 8q^{79} - 28q^{80} - 24q^{81} - 256q^{82} + 144q^{83} - 52q^{84} - 184q^{86} + 44q^{87} - 40q^{88} + 80q^{89} - 204q^{90} + 112q^{91} - 72q^{92} + 104q^{93} - 256q^{94} + 144q^{95} - 18q^{96} + 48q^{97} - 48q^{98} - 40q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1470))$$

We only show spaces with even 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
1470.2.a $$\chi_{1470}(1, \cdot)$$ 1470.2.a.a 1 1
1470.2.a.b 1
1470.2.a.c 1
1470.2.a.d 1
1470.2.a.e 1
1470.2.a.f 1
1470.2.a.g 1
1470.2.a.h 1
1470.2.a.i 1
1470.2.a.j 1
1470.2.a.k 1
1470.2.a.l 1
1470.2.a.m 1
1470.2.a.n 1
1470.2.a.o 1
1470.2.a.p 1
1470.2.a.q 1
1470.2.a.r 1
1470.2.a.s 2
1470.2.a.t 2
1470.2.a.u 2
1470.2.a.v 2
1470.2.b $$\chi_{1470}(881, \cdot)$$ 1470.2.b.a 12 1
1470.2.b.b 12
1470.2.b.c 16
1470.2.b.d 16
1470.2.d $$\chi_{1470}(1469, \cdot)$$ 1470.2.d.a 4 1
1470.2.d.b 4
1470.2.d.c 4
1470.2.d.d 4
1470.2.d.e 8
1470.2.d.f 8
1470.2.d.g 24
1470.2.d.h 24
1470.2.g $$\chi_{1470}(589, \cdot)$$ 1470.2.g.a 2 1
1470.2.g.b 2
1470.2.g.c 2
1470.2.g.d 2
1470.2.g.e 2
1470.2.g.f 2
1470.2.g.g 2
1470.2.g.h 6
1470.2.g.i 6
1470.2.g.j 8
1470.2.g.k 8
1470.2.i $$\chi_{1470}(361, \cdot)$$ 1470.2.i.a 2 2
1470.2.i.b 2
1470.2.i.c 2
1470.2.i.d 2
1470.2.i.e 2
1470.2.i.f 2
1470.2.i.g 2
1470.2.i.h 2
1470.2.i.i 2
1470.2.i.j 2
1470.2.i.k 2
1470.2.i.l 2
1470.2.i.m 2
1470.2.i.n 2
1470.2.i.o 2
1470.2.i.p 2
1470.2.i.q 2
1470.2.i.r 2
1470.2.i.s 2
1470.2.i.t 2
1470.2.i.u 4
1470.2.i.v 4
1470.2.i.w 4
1470.2.i.x 4
1470.2.j $$\chi_{1470}(197, \cdot)$$ n/a 164 2
1470.2.m $$\chi_{1470}(97, \cdot)$$ 1470.2.m.a 8 2
1470.2.m.b 8
1470.2.m.c 16
1470.2.m.d 16
1470.2.m.e 16
1470.2.m.f 16
1470.2.n $$\chi_{1470}(79, \cdot)$$ 1470.2.n.a 4 2
1470.2.n.b 4
1470.2.n.c 4
1470.2.n.d 4
1470.2.n.e 4
1470.2.n.f 4
1470.2.n.g 4
1470.2.n.h 4
1470.2.n.i 4
1470.2.n.j 12
1470.2.n.k 16
1470.2.n.l 16
1470.2.r $$\chi_{1470}(521, \cdot)$$ n/a 104 2
1470.2.t $$\chi_{1470}(509, \cdot)$$ n/a 160 2
1470.2.u $$\chi_{1470}(211, \cdot)$$ n/a 240 6
1470.2.v $$\chi_{1470}(313, \cdot)$$ n/a 160 4
1470.2.y $$\chi_{1470}(263, \cdot)$$ n/a 320 4
1470.2.bb $$\chi_{1470}(169, \cdot)$$ n/a 336 6
1470.2.bc $$\chi_{1470}(209, \cdot)$$ n/a 672 6
1470.2.be $$\chi_{1470}(41, \cdot)$$ n/a 432 6
1470.2.bg $$\chi_{1470}(121, \cdot)$$ n/a 432 12
1470.2.bi $$\chi_{1470}(13, \cdot)$$ n/a 672 12
1470.2.bj $$\chi_{1470}(113, \cdot)$$ n/a 1344 12
1470.2.bm $$\chi_{1470}(59, \cdot)$$ n/a 1344 12
1470.2.bo $$\chi_{1470}(101, \cdot)$$ n/a 912 12
1470.2.bq $$\chi_{1470}(109, \cdot)$$ n/a 672 12
1470.2.bt $$\chi_{1470}(23, \cdot)$$ n/a 2688 24
1470.2.bu $$\chi_{1470}(73, \cdot)$$ n/a 1344 24

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1470))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1470)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 2}$$