# Properties

 Label 1050.3 Level 1050 Weight 3 Dimension 12720 Nonzero newspaces 24 Sturm bound 172800 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$24$$ Sturm bound: $$172800$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1050))$$.

Total New Old
Modular forms 58944 12720 46224
Cusp forms 56256 12720 43536
Eisenstein series 2688 0 2688

## Trace form

 $$12720q + 16q^{2} + 22q^{3} + 8q^{4} - 32q^{6} - 32q^{7} - 32q^{8} - 142q^{9} + O(q^{10})$$ $$12720q + 16q^{2} + 22q^{3} + 8q^{4} - 32q^{6} - 32q^{7} - 32q^{8} - 142q^{9} - 24q^{10} - 100q^{11} - 44q^{12} - 140q^{13} + 8q^{15} + 64q^{16} - 432q^{17} + 32q^{18} - 520q^{19} - 64q^{20} - 10q^{21} - 192q^{22} - 176q^{23} + 24q^{24} - 120q^{25} - 416q^{26} - 644q^{27} - 312q^{28} - 40q^{29} + 192q^{30} - 152q^{31} + 96q^{32} + 282q^{33} + 360q^{34} + 472q^{35} + 24q^{36} - 132q^{37} + 536q^{38} + 156q^{39} - 48q^{40} + 832q^{41} + 920q^{42} + 1248q^{43} + 888q^{44} + 32q^{45} + 1400q^{46} + 1180q^{47} + 64q^{48} + 348q^{49} + 184q^{50} + 758q^{51} + 280q^{52} + 1024q^{53} + 816q^{54} + 1216q^{55} + 32q^{56} + 676q^{57} - 128q^{58} - 344q^{59} + 416q^{60} - 2256q^{61} - 320q^{62} + 1046q^{63} - 64q^{64} - 664q^{65} + 16q^{66} - 1592q^{67} - 256q^{68} + 852q^{69} - 48q^{70} + 832q^{71} - 112q^{72} + 1964q^{73} + 240q^{74} - 232q^{75} + 8q^{76} + 2192q^{77} + 32q^{78} + 2384q^{79} - 442q^{81} + 1136q^{82} + 2176q^{83} - 132q^{84} + 48q^{85} + 120q^{86} + 196q^{87} - 400q^{88} - 272q^{89} - 504q^{90} - 672q^{91} - 176q^{92} + 1654q^{93} - 1736q^{94} - 512q^{95} + 208q^{96} + 1104q^{97} - 48q^{98} + 2324q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1050))$$

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
1050.3.c $$\chi_{1050}(449, \cdot)$$ 1050.3.c.a 8 1
1050.3.c.b 32
1050.3.c.c 32
1050.3.e $$\chi_{1050}(701, \cdot)$$ 1050.3.e.a 4 1
1050.3.e.b 16
1050.3.e.c 16
1050.3.e.d 16
1050.3.e.e 24
1050.3.f $$\chi_{1050}(601, \cdot)$$ 1050.3.f.a 4 1
1050.3.f.b 8
1050.3.f.c 12
1050.3.f.d 12
1050.3.f.e 16
1050.3.h $$\chi_{1050}(349, \cdot)$$ 1050.3.h.a 8 1
1050.3.h.b 16
1050.3.h.c 24
1050.3.k $$\chi_{1050}(293, \cdot)$$ n/a 192 2
1050.3.l $$\chi_{1050}(43, \cdot)$$ 1050.3.l.a 8 2
1050.3.l.b 8
1050.3.l.c 8
1050.3.l.d 8
1050.3.l.e 8
1050.3.l.f 8
1050.3.l.g 8
1050.3.l.h 16
1050.3.p $$\chi_{1050}(451, \cdot)$$ 1050.3.p.a 4 2
1050.3.p.b 8
1050.3.p.c 8
1050.3.p.d 8
1050.3.p.e 12
1050.3.p.f 12
1050.3.p.g 16
1050.3.p.h 16
1050.3.p.i 16
1050.3.q $$\chi_{1050}(199, \cdot)$$ 1050.3.q.a 8 2
1050.3.q.b 16
1050.3.q.c 16
1050.3.q.d 24
1050.3.q.e 32
1050.3.r $$\chi_{1050}(149, \cdot)$$ n/a 192 2
1050.3.t $$\chi_{1050}(401, \cdot)$$ n/a 204 2
1050.3.v $$\chi_{1050}(139, \cdot)$$ n/a 320 4
1050.3.x $$\chi_{1050}(181, \cdot)$$ n/a 320 4
1050.3.y $$\chi_{1050}(71, \cdot)$$ n/a 480 4
1050.3.ba $$\chi_{1050}(29, \cdot)$$ n/a 480 4
1050.3.bd $$\chi_{1050}(193, \cdot)$$ n/a 192 4
1050.3.be $$\chi_{1050}(143, \cdot)$$ n/a 384 4
1050.3.bi $$\chi_{1050}(127, \cdot)$$ n/a 480 8
1050.3.bj $$\chi_{1050}(83, \cdot)$$ n/a 1280 8
1050.3.bm $$\chi_{1050}(11, \cdot)$$ n/a 1280 8
1050.3.bo $$\chi_{1050}(179, \cdot)$$ n/a 1280 8
1050.3.bp $$\chi_{1050}(19, \cdot)$$ n/a 640 8
1050.3.bq $$\chi_{1050}(31, \cdot)$$ n/a 640 8
1050.3.bt $$\chi_{1050}(17, \cdot)$$ n/a 2560 16
1050.3.bu $$\chi_{1050}(37, \cdot)$$ n/a 1280 16

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1050))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(1050)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 2}$$