# Properties

 Label 1320.2 Level 1320 Weight 2 Dimension 17308 Nonzero newspaces 36 Sturm bound 184320 Trace bound 22

## Defining parameters

 Level: $$N$$ = $$1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$184320$$ Trace bound: $$22$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1320))$$.

Total New Old
Modular forms 48000 17740 30260
Cusp forms 44161 17308 26853
Eisenstein series 3839 432 3407

## Trace form

 $$17308 q - 8 q^{2} - 24 q^{3} - 40 q^{4} - 8 q^{5} - 36 q^{6} - 56 q^{7} + 16 q^{8} - 40 q^{9} + O(q^{10})$$ $$17308 q - 8 q^{2} - 24 q^{3} - 40 q^{4} - 8 q^{5} - 36 q^{6} - 56 q^{7} + 16 q^{8} - 40 q^{9} - 36 q^{10} + 24 q^{12} - 16 q^{13} + 64 q^{14} - 4 q^{15} - 24 q^{16} - 40 q^{17} + 20 q^{18} - 20 q^{19} + 64 q^{20} - 8 q^{21} - 8 q^{22} + 8 q^{23} - 4 q^{24} - 144 q^{25} + 32 q^{26} + 72 q^{27} - 40 q^{28} + 8 q^{29} + 8 q^{30} - 16 q^{31} - 8 q^{32} + 30 q^{33} + 48 q^{34} + 156 q^{35} + 116 q^{36} + 80 q^{37} + 120 q^{38} + 140 q^{39} - 48 q^{40} + 120 q^{41} + 136 q^{42} + 168 q^{43} + 224 q^{44} + 6 q^{45} + 32 q^{46} + 88 q^{47} + 56 q^{48} + 88 q^{49} + 36 q^{50} - 50 q^{51} + 176 q^{52} - 32 q^{53} + 68 q^{54} + 16 q^{55} + 128 q^{56} + 70 q^{57} - 32 q^{58} - 48 q^{59} - 124 q^{60} - 96 q^{61} - 16 q^{62} - 68 q^{63} - 136 q^{64} + 32 q^{65} - 124 q^{66} - 128 q^{67} - 112 q^{68} + 80 q^{69} - 344 q^{70} + 48 q^{71} - 204 q^{72} + 200 q^{73} - 312 q^{74} - 24 q^{75} - 504 q^{76} + 120 q^{77} - 424 q^{78} + 232 q^{79} - 380 q^{80} + 16 q^{81} - 696 q^{82} + 240 q^{83} - 404 q^{84} + 248 q^{85} - 288 q^{86} + 80 q^{87} - 632 q^{88} + 200 q^{89} - 122 q^{90} + 528 q^{91} - 304 q^{92} + 244 q^{93} - 264 q^{94} + 272 q^{95} - 96 q^{96} + 268 q^{97} - 240 q^{98} + 72 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1320))$$

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
1320.2.a $$\chi_{1320}(1, \cdot)$$ 1320.2.a.a 1 1
1320.2.a.b 1
1320.2.a.c 1
1320.2.a.d 1
1320.2.a.e 1
1320.2.a.f 1
1320.2.a.g 1
1320.2.a.h 1
1320.2.a.i 1
1320.2.a.j 1
1320.2.a.k 1
1320.2.a.l 1
1320.2.a.m 1
1320.2.a.n 1
1320.2.a.o 2
1320.2.a.p 2
1320.2.a.q 2
1320.2.d $$\chi_{1320}(529, \cdot)$$ 1320.2.d.a 6 1
1320.2.d.b 6
1320.2.d.c 10
1320.2.d.d 10
1320.2.e $$\chi_{1320}(1211, \cdot)$$ n/a 160 1
1320.2.f $$\chi_{1320}(1121, \cdot)$$ 1320.2.f.a 24 1
1320.2.f.b 24
1320.2.g $$\chi_{1320}(1099, \cdot)$$ n/a 144 1
1320.2.j $$\chi_{1320}(1189, \cdot)$$ n/a 120 1
1320.2.k $$\chi_{1320}(551, \cdot)$$ None 0 1
1320.2.p $$\chi_{1320}(461, \cdot)$$ n/a 192 1
1320.2.q $$\chi_{1320}(439, \cdot)$$ None 0 1
1320.2.t $$\chi_{1320}(1231, \cdot)$$ None 0 1
1320.2.u $$\chi_{1320}(989, \cdot)$$ n/a 280 1
1320.2.v $$\chi_{1320}(1079, \cdot)$$ None 0 1
1320.2.w $$\chi_{1320}(661, \cdot)$$ 1320.2.w.a 2 1
1320.2.w.b 2
1320.2.w.c 12
1320.2.w.d 18
1320.2.w.e 20
1320.2.w.f 26
1320.2.z $$\chi_{1320}(571, \cdot)$$ 1320.2.z.a 4 1
1320.2.z.b 4
1320.2.z.c 40
1320.2.z.d 48
1320.2.ba $$\chi_{1320}(329, \cdot)$$ 1320.2.ba.a 72 1
1320.2.bf $$\chi_{1320}(419, \cdot)$$ n/a 240 1
1320.2.bh $$\chi_{1320}(263, \cdot)$$ None 0 2
1320.2.bi $$\chi_{1320}(373, \cdot)$$ n/a 288 2
1320.2.bl $$\chi_{1320}(67, \cdot)$$ n/a 240 2
1320.2.bm $$\chi_{1320}(353, \cdot)$$ n/a 120 2
1320.2.bp $$\chi_{1320}(463, \cdot)$$ None 0 2
1320.2.bq $$\chi_{1320}(1013, \cdot)$$ n/a 480 2
1320.2.bt $$\chi_{1320}(923, \cdot)$$ n/a 560 2
1320.2.bu $$\chi_{1320}(1033, \cdot)$$ 1320.2.bu.a 36 2
1320.2.bu.b 36
1320.2.bw $$\chi_{1320}(361, \cdot)$$ 1320.2.bw.a 4 4
1320.2.bw.b 8
1320.2.bw.c 8
1320.2.bw.d 12
1320.2.bw.e 12
1320.2.bw.f 12
1320.2.bw.g 12
1320.2.bw.h 12
1320.2.bw.i 16
1320.2.bx $$\chi_{1320}(59, \cdot)$$ n/a 1120 4
1320.2.cc $$\chi_{1320}(211, \cdot)$$ n/a 384 4
1320.2.cd $$\chi_{1320}(569, \cdot)$$ n/a 288 4
1320.2.cg $$\chi_{1320}(119, \cdot)$$ None 0 4
1320.2.ch $$\chi_{1320}(181, \cdot)$$ n/a 384 4
1320.2.ci $$\chi_{1320}(151, \cdot)$$ None 0 4
1320.2.cj $$\chi_{1320}(29, \cdot)$$ n/a 1120 4
1320.2.cm $$\chi_{1320}(101, \cdot)$$ n/a 768 4
1320.2.cn $$\chi_{1320}(79, \cdot)$$ None 0 4
1320.2.cs $$\chi_{1320}(229, \cdot)$$ n/a 576 4
1320.2.ct $$\chi_{1320}(71, \cdot)$$ None 0 4
1320.2.cw $$\chi_{1320}(41, \cdot)$$ n/a 192 4
1320.2.cx $$\chi_{1320}(19, \cdot)$$ n/a 576 4
1320.2.cy $$\chi_{1320}(49, \cdot)$$ n/a 144 4
1320.2.cz $$\chi_{1320}(251, \cdot)$$ n/a 768 4
1320.2.dd $$\chi_{1320}(73, \cdot)$$ n/a 288 8
1320.2.de $$\chi_{1320}(83, \cdot)$$ n/a 2240 8
1320.2.dh $$\chi_{1320}(53, \cdot)$$ n/a 2240 8
1320.2.di $$\chi_{1320}(103, \cdot)$$ None 0 8
1320.2.dl $$\chi_{1320}(113, \cdot)$$ n/a 576 8
1320.2.dm $$\chi_{1320}(163, \cdot)$$ n/a 1152 8
1320.2.dp $$\chi_{1320}(13, \cdot)$$ n/a 1152 8
1320.2.dq $$\chi_{1320}(167, \cdot)$$ None 0 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1320))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1320)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(330))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(660))$$$$^{\oplus 2}$$