# Properties

 Label 2169.2 Level 2169 Weight 2 Dimension 136860 Nonzero newspaces 50 Sturm bound 696960 Trace bound 16

## Defining parameters

 Level: $$N$$ = $$2169 = 3^{2} \cdot 241$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$50$$ Sturm bound: $$696960$$ Trace bound: $$16$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2169))$$.

Total New Old
Modular forms 176160 139010 37150
Cusp forms 172321 136860 35461
Eisenstein series 3839 2150 1689

## Trace form

 $$136860q - 360q^{2} - 480q^{3} - 360q^{4} - 360q^{5} - 480q^{6} - 360q^{7} - 360q^{8} - 480q^{9} + O(q^{10})$$ $$136860q - 360q^{2} - 480q^{3} - 360q^{4} - 360q^{5} - 480q^{6} - 360q^{7} - 360q^{8} - 480q^{9} - 1080q^{10} - 360q^{11} - 480q^{12} - 360q^{13} - 360q^{14} - 480q^{15} - 360q^{16} - 360q^{17} - 480q^{18} - 1080q^{19} - 360q^{20} - 480q^{21} - 360q^{22} - 360q^{23} - 480q^{24} - 360q^{25} - 360q^{26} - 480q^{27} - 1080q^{28} - 360q^{29} - 480q^{30} - 360q^{31} - 360q^{32} - 480q^{33} - 360q^{34} - 360q^{35} - 480q^{36} - 1080q^{37} - 360q^{38} - 480q^{39} - 360q^{40} - 360q^{41} - 480q^{42} - 360q^{43} - 360q^{44} - 480q^{45} - 1080q^{46} - 360q^{47} - 480q^{48} - 360q^{49} - 360q^{50} - 480q^{51} - 360q^{52} - 360q^{53} - 480q^{54} - 1080q^{55} - 360q^{56} - 480q^{57} - 360q^{58} - 360q^{59} - 480q^{60} - 360q^{61} - 360q^{62} - 480q^{63} - 1080q^{64} - 360q^{65} - 480q^{66} - 360q^{67} - 360q^{68} - 480q^{69} - 360q^{70} - 360q^{71} - 480q^{72} - 1080q^{73} - 360q^{74} - 480q^{75} - 360q^{76} - 360q^{77} - 480q^{78} - 360q^{79} - 360q^{80} - 480q^{81} - 1080q^{82} - 360q^{83} - 480q^{84} - 360q^{85} - 360q^{86} - 480q^{87} - 360q^{88} - 360q^{89} - 480q^{90} - 1080q^{91} - 360q^{92} - 480q^{93} - 360q^{94} - 360q^{95} - 480q^{96} - 360q^{97} - 360q^{98} - 480q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2169))$$

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
2169.2.a $$\chi_{2169}(1, \cdot)$$ 2169.2.a.a 1 1
2169.2.a.b 1
2169.2.a.c 2
2169.2.a.d 5
2169.2.a.e 7
2169.2.a.f 9
2169.2.a.g 10
2169.2.a.h 12
2169.2.a.i 13
2169.2.a.j 14
2169.2.a.k 26
2169.2.d $$\chi_{2169}(1927, \cdot)$$ 2169.2.d.a 4 1
2169.2.d.b 4
2169.2.d.c 16
2169.2.d.d 18
2169.2.d.e 22
2169.2.d.f 36
2169.2.e $$\chi_{2169}(256, \cdot)$$ n/a 480 2
2169.2.f $$\chi_{2169}(724, \cdot)$$ n/a 480 2
2169.2.g $$\chi_{2169}(1189, \cdot)$$ n/a 198 2
2169.2.h $$\chi_{2169}(979, \cdot)$$ n/a 480 2
2169.2.i $$\chi_{2169}(64, \cdot)$$ n/a 200 2
2169.2.k $$\chi_{2169}(91, \cdot)$$ n/a 400 4
2169.2.n $$\chi_{2169}(16, \cdot)$$ n/a 480 2
2169.2.o $$\chi_{2169}(481, \cdot)$$ n/a 480 2
2169.2.p $$\chi_{2169}(226, \cdot)$$ n/a 198 2
2169.2.w $$\chi_{2169}(1462, \cdot)$$ n/a 480 2
2169.2.x $$\chi_{2169}(271, \cdot)$$ n/a 404 4
2169.2.bb $$\chi_{2169}(154, \cdot)$$ n/a 400 4
2169.2.bc $$\chi_{2169}(301, \cdot)$$ n/a 960 4
2169.2.bg $$\chi_{2169}(181, \cdot)$$ n/a 396 4
2169.2.bh $$\chi_{2169}(4, \cdot)$$ n/a 960 4
2169.2.bi $$\chi_{2169}(418, \cdot)$$ n/a 960 4
2169.2.bk $$\chi_{2169}(100, \cdot)$$ n/a 792 8
2169.2.bl $$\chi_{2169}(205, \cdot)$$ n/a 1920 8
2169.2.bm $$\chi_{2169}(265, \cdot)$$ n/a 1920 8
2169.2.bn $$\chi_{2169}(94, \cdot)$$ n/a 1920 8
2169.2.bo $$\chi_{2169}(44, \cdot)$$ n/a 656 8
2169.2.bq $$\chi_{2169}(235, \cdot)$$ n/a 800 8
2169.2.bs $$\chi_{2169}(691, \cdot)$$ n/a 1920 8
2169.2.bv $$\chi_{2169}(361, \cdot)$$ n/a 800 8
2169.2.bx $$\chi_{2169}(121, \cdot)$$ n/a 1920 8
2169.2.bz $$\chi_{2169}(211, \cdot)$$ n/a 1920 8
2169.2.cc $$\chi_{2169}(10, \cdot)$$ n/a 792 8
2169.2.cd $$\chi_{2169}(277, \cdot)$$ n/a 1920 8
2169.2.ce $$\chi_{2169}(58, \cdot)$$ n/a 1920 8
2169.2.cl $$\chi_{2169}(322, \cdot)$$ n/a 1920 8
2169.2.cn $$\chi_{2169}(289, \cdot)$$ n/a 1616 16
2169.2.co $$\chi_{2169}(317, \cdot)$$ n/a 3840 16
2169.2.cq $$\chi_{2169}(38, \cdot)$$ n/a 3840 16
2169.2.cs $$\chi_{2169}(89, \cdot)$$ n/a 1280 16
2169.2.cu $$\chi_{2169}(11, \cdot)$$ n/a 3840 16
2169.2.cw $$\chi_{2169}(97, \cdot)$$ n/a 3840 16
2169.2.da $$\chi_{2169}(25, \cdot)$$ n/a 3840 16
2169.2.db $$\chi_{2169}(232, \cdot)$$ n/a 3840 16
2169.2.dc $$\chi_{2169}(82, \cdot)$$ n/a 1584 16
2169.2.df $$\chi_{2169}(17, \cdot)$$ n/a 2624 32
2169.2.dh $$\chi_{2169}(67, \cdot)$$ n/a 7680 32
2169.2.di $$\chi_{2169}(61, \cdot)$$ n/a 7680 32
2169.2.dk $$\chi_{2169}(49, \cdot)$$ n/a 7680 32
2169.2.dm $$\chi_{2169}(244, \cdot)$$ n/a 3200 32
2169.2.dp $$\chi_{2169}(74, \cdot)$$ n/a 15360 64
2169.2.dr $$\chi_{2169}(14, \cdot)$$ n/a 15360 64
2169.2.dt $$\chi_{2169}(35, \cdot)$$ n/a 5120 64
2169.2.dv $$\chi_{2169}(23, \cdot)$$ n/a 15360 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2169))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2169)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(241))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(723))$$$$^{\oplus 2}$$