# Properties

 Label 3344.2 Level 3344 Weight 2 Dimension 188720 Nonzero newspaces 48 Sturm bound 1382400 Trace bound 41

## Defining parameters

 Level: $$N$$ = $$3344 = 2^{4} \cdot 11 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$1382400$$ Trace bound: $$41$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3344))$$.

Total New Old
Modular forms 350640 191476 159164
Cusp forms 340561 188720 151841
Eisenstein series 10079 2756 7323

## Trace form

 $$188720 q - 256 q^{2} - 194 q^{3} - 248 q^{4} - 318 q^{5} - 232 q^{6} - 186 q^{7} - 232 q^{8} - 62 q^{9} + O(q^{10})$$ $$188720 q - 256 q^{2} - 194 q^{3} - 248 q^{4} - 318 q^{5} - 232 q^{6} - 186 q^{7} - 232 q^{8} - 62 q^{9} - 248 q^{10} - 209 q^{11} - 584 q^{12} - 318 q^{13} - 264 q^{14} - 170 q^{15} - 280 q^{16} - 574 q^{17} - 240 q^{18} - 189 q^{19} - 520 q^{20} - 284 q^{21} - 284 q^{22} - 426 q^{23} - 248 q^{24} - 62 q^{25} - 232 q^{26} - 218 q^{27} - 216 q^{28} - 286 q^{29} - 264 q^{30} - 250 q^{31} - 216 q^{32} - 607 q^{33} - 552 q^{34} - 142 q^{35} - 264 q^{36} - 228 q^{37} - 292 q^{38} - 282 q^{39} - 280 q^{40} + 18 q^{41} - 248 q^{42} - 96 q^{43} - 292 q^{44} - 582 q^{45} - 200 q^{46} - 62 q^{47} - 216 q^{48} - 454 q^{49} - 272 q^{50} - 50 q^{51} - 264 q^{52} - 310 q^{53} - 248 q^{54} - 153 q^{55} - 600 q^{56} - 47 q^{57} - 584 q^{58} - 210 q^{59} - 248 q^{60} - 310 q^{61} - 184 q^{62} - 56 q^{63} - 248 q^{64} - 388 q^{65} - 276 q^{66} - 250 q^{67} - 248 q^{68} - 184 q^{69} - 496 q^{70} - 98 q^{71} - 432 q^{72} - 6 q^{73} - 448 q^{74} - 8 q^{75} - 404 q^{76} - 804 q^{77} - 1064 q^{78} - 34 q^{79} - 656 q^{80} - 542 q^{81} - 648 q^{82} - 186 q^{83} - 760 q^{84} - 470 q^{85} - 568 q^{86} - 140 q^{87} - 908 q^{88} - 158 q^{89} - 904 q^{90} - 146 q^{91} - 664 q^{92} - 494 q^{93} - 792 q^{94} - 275 q^{95} - 1000 q^{96} - 814 q^{97} - 712 q^{98} - 317 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3344))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
3344.2.a $$\chi_{3344}(1, \cdot)$$ 3344.2.a.a 1 1
3344.2.a.b 1
3344.2.a.c 1
3344.2.a.d 1
3344.2.a.e 1
3344.2.a.f 1
3344.2.a.g 1
3344.2.a.h 1
3344.2.a.i 1
3344.2.a.j 2
3344.2.a.k 2
3344.2.a.l 2
3344.2.a.m 2
3344.2.a.n 2
3344.2.a.o 2
3344.2.a.p 3
3344.2.a.q 3
3344.2.a.r 3
3344.2.a.s 4
3344.2.a.t 5
3344.2.a.u 5
3344.2.a.v 6
3344.2.a.w 6
3344.2.a.x 6
3344.2.a.y 6
3344.2.a.z 6
3344.2.a.ba 7
3344.2.a.bb 9
3344.2.c $$\chi_{3344}(3191, \cdot)$$ None 0 1
3344.2.e $$\chi_{3344}(1673, \cdot)$$ None 0 1
3344.2.f $$\chi_{3344}(417, \cdot)$$ n/a 118 1
3344.2.h $$\chi_{3344}(1407, \cdot)$$ n/a 108 1
3344.2.j $$\chi_{3344}(2089, \cdot)$$ None 0 1
3344.2.l $$\chi_{3344}(3079, \cdot)$$ None 0 1
3344.2.o $$\chi_{3344}(1519, \cdot)$$ 3344.2.o.a 36 1
3344.2.o.b 64
3344.2.q $$\chi_{3344}(353, \cdot)$$ n/a 200 2
3344.2.r $$\chi_{3344}(571, \cdot)$$ n/a 864 2
3344.2.u $$\chi_{3344}(837, \cdot)$$ n/a 720 2
3344.2.v $$\chi_{3344}(1253, \cdot)$$ n/a 952 2
3344.2.y $$\chi_{3344}(683, \cdot)$$ n/a 800 2
3344.2.z $$\chi_{3344}(609, \cdot)$$ n/a 432 4
3344.2.ba $$\chi_{3344}(639, \cdot)$$ n/a 200 2
3344.2.be $$\chi_{3344}(1209, \cdot)$$ None 0 2
3344.2.bg $$\chi_{3344}(87, \cdot)$$ None 0 2
3344.2.bi $$\chi_{3344}(65, \cdot)$$ n/a 236 2
3344.2.bk $$\chi_{3344}(1759, \cdot)$$ n/a 240 2
3344.2.bl $$\chi_{3344}(2311, \cdot)$$ None 0 2
3344.2.bn $$\chi_{3344}(2025, \cdot)$$ None 0 2
3344.2.bp $$\chi_{3344}(177, \cdot)$$ n/a 600 6
3344.2.br $$\chi_{3344}(911, \cdot)$$ n/a 480 4
3344.2.bu $$\chi_{3344}(39, \cdot)$$ None 0 4
3344.2.bw $$\chi_{3344}(569, \cdot)$$ None 0 4
3344.2.by $$\chi_{3344}(799, \cdot)$$ n/a 432 4
3344.2.ca $$\chi_{3344}(721, \cdot)$$ n/a 472 4
3344.2.cb $$\chi_{3344}(1065, \cdot)$$ None 0 4
3344.2.cd $$\chi_{3344}(455, \cdot)$$ None 0 4
3344.2.cf $$\chi_{3344}(45, \cdot)$$ n/a 1600 4
3344.2.ci $$\chi_{3344}(923, \cdot)$$ n/a 1904 4
3344.2.cj $$\chi_{3344}(331, \cdot)$$ n/a 1600 4
3344.2.cm $$\chi_{3344}(373, \cdot)$$ n/a 1904 4
3344.2.cn $$\chi_{3344}(49, \cdot)$$ n/a 944 8
3344.2.cp $$\chi_{3344}(263, \cdot)$$ None 0 6
3344.2.cr $$\chi_{3344}(441, \cdot)$$ None 0 6
3344.2.cu $$\chi_{3344}(175, \cdot)$$ n/a 720 6
3344.2.cv $$\chi_{3344}(287, \cdot)$$ n/a 600 6
3344.2.cy $$\chi_{3344}(857, \cdot)$$ None 0 6
3344.2.da $$\chi_{3344}(375, \cdot)$$ None 0 6
3344.2.db $$\chi_{3344}(241, \cdot)$$ n/a 708 6
3344.2.dd $$\chi_{3344}(75, \cdot)$$ n/a 3808 8
3344.2.dg $$\chi_{3344}(189, \cdot)$$ n/a 3808 8
3344.2.dh $$\chi_{3344}(229, \cdot)$$ n/a 3456 8
3344.2.dk $$\chi_{3344}(723, \cdot)$$ n/a 3456 8
3344.2.dm $$\chi_{3344}(201, \cdot)$$ None 0 8
3344.2.do $$\chi_{3344}(103, \cdot)$$ None 0 8
3344.2.dp $$\chi_{3344}(239, \cdot)$$ n/a 960 8
3344.2.dr $$\chi_{3344}(145, \cdot)$$ n/a 944 8
3344.2.dt $$\chi_{3344}(7, \cdot)$$ None 0 8
3344.2.dv $$\chi_{3344}(217, \cdot)$$ None 0 8
3344.2.dz $$\chi_{3344}(31, \cdot)$$ n/a 960 8
3344.2.ea $$\chi_{3344}(67, \cdot)$$ n/a 4800 12
3344.2.ec $$\chi_{3344}(21, \cdot)$$ n/a 5712 12
3344.2.ef $$\chi_{3344}(309, \cdot)$$ n/a 4800 12
3344.2.eh $$\chi_{3344}(43, \cdot)$$ n/a 5712 12
3344.2.ei $$\chi_{3344}(81, \cdot)$$ n/a 2832 24
3344.2.ej $$\chi_{3344}(293, \cdot)$$ n/a 7616 16
3344.2.em $$\chi_{3344}(27, \cdot)$$ n/a 7616 16
3344.2.en $$\chi_{3344}(83, \cdot)$$ n/a 7616 16
3344.2.eq $$\chi_{3344}(125, \cdot)$$ n/a 7616 16
3344.2.es $$\chi_{3344}(129, \cdot)$$ n/a 2832 24
3344.2.et $$\chi_{3344}(71, \cdot)$$ None 0 24
3344.2.ev $$\chi_{3344}(41, \cdot)$$ None 0 24
3344.2.ey $$\chi_{3344}(15, \cdot)$$ n/a 2880 24
3344.2.ez $$\chi_{3344}(63, \cdot)$$ n/a 2880 24
3344.2.fc $$\chi_{3344}(9, \cdot)$$ None 0 24
3344.2.fe $$\chi_{3344}(215, \cdot)$$ None 0 24
3344.2.fg $$\chi_{3344}(35, \cdot)$$ n/a 22848 48
3344.2.fi $$\chi_{3344}(5, \cdot)$$ n/a 22848 48
3344.2.fl $$\chi_{3344}(13, \cdot)$$ n/a 22848 48
3344.2.fn $$\chi_{3344}(3, \cdot)$$ n/a 22848 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3344))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3344)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(418))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(836))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1672))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3344))$$$$^{\oplus 1}$$