# Properties

 Label 1368.4 Level 1368 Weight 4 Dimension 68563 Nonzero newspaces 48 Sturm bound 414720 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$1368 = 2^{3} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$48$$ Sturm bound: $$414720$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1368))$$.

Total New Old
Modular forms 157248 69175 88073
Cusp forms 153792 68563 85229
Eisenstein series 3456 612 2844

## Trace form

 $$68563 q - 46 q^{2} - 66 q^{3} - 26 q^{4} + 44 q^{5} - 32 q^{6} + 30 q^{7} - 106 q^{8} - 186 q^{9} + O(q^{10})$$ $$68563 q - 46 q^{2} - 66 q^{3} - 26 q^{4} + 44 q^{5} - 32 q^{6} + 30 q^{7} - 106 q^{8} - 186 q^{9} - 322 q^{10} - 268 q^{11} - 284 q^{12} - 128 q^{13} - 346 q^{14} - 120 q^{15} - 322 q^{16} + 176 q^{17} + 168 q^{18} + 24 q^{19} + 800 q^{20} - 456 q^{21} + 1190 q^{22} - 546 q^{23} + 456 q^{24} - 126 q^{25} - 118 q^{26} - 648 q^{27} + 142 q^{28} - 246 q^{29} - 308 q^{30} - 80 q^{31} - 386 q^{32} + 794 q^{33} - 2818 q^{34} + 1950 q^{35} + 1460 q^{36} + 1002 q^{37} - 448 q^{38} + 408 q^{39} - 1674 q^{40} + 1736 q^{41} + 164 q^{42} + 3212 q^{43} + 2022 q^{44} - 892 q^{45} + 5230 q^{46} + 1644 q^{47} + 1520 q^{48} - 3224 q^{49} + 6182 q^{50} - 762 q^{51} + 3070 q^{52} - 3880 q^{53} - 1320 q^{54} - 3762 q^{55} - 5302 q^{56} - 1681 q^{57} - 9704 q^{58} - 8752 q^{59} - 1668 q^{60} + 3634 q^{61} + 976 q^{62} - 2440 q^{63} + 4246 q^{64} + 2074 q^{65} - 5072 q^{66} + 1248 q^{67} + 1272 q^{68} + 7420 q^{69} + 3030 q^{70} + 9040 q^{71} - 1980 q^{72} - 3093 q^{73} - 7570 q^{74} + 11686 q^{75} - 12312 q^{76} - 1422 q^{77} - 7964 q^{78} - 15584 q^{79} - 24294 q^{80} - 4018 q^{81} - 26880 q^{82} - 15824 q^{83} - 376 q^{84} - 2488 q^{85} + 4064 q^{86} - 14172 q^{87} + 2750 q^{88} - 3562 q^{89} - 3812 q^{90} + 15894 q^{91} + 19584 q^{92} - 7492 q^{93} + 19662 q^{94} + 29686 q^{95} + 7920 q^{96} + 18186 q^{97} + 20598 q^{98} + 27066 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1368))$$

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
1368.4.a $$\chi_{1368}(1, \cdot)$$ 1368.4.a.a 2 1
1368.4.a.b 2
1368.4.a.c 2
1368.4.a.d 3
1368.4.a.e 3
1368.4.a.f 3
1368.4.a.g 4
1368.4.a.h 4
1368.4.a.i 4
1368.4.a.j 4
1368.4.a.k 5
1368.4.a.l 5
1368.4.a.m 5
1368.4.a.n 5
1368.4.a.o 8
1368.4.a.p 8
1368.4.d $$\chi_{1368}(647, \cdot)$$ None 0 1
1368.4.e $$\chi_{1368}(379, \cdot)$$ n/a 298 1
1368.4.f $$\chi_{1368}(1025, \cdot)$$ 1368.4.f.a 30 1
1368.4.f.b 30
1368.4.g $$\chi_{1368}(685, \cdot)$$ n/a 270 1
1368.4.j $$\chi_{1368}(1331, \cdot)$$ n/a 216 1
1368.4.k $$\chi_{1368}(1063, \cdot)$$ None 0 1
1368.4.p $$\chi_{1368}(341, \cdot)$$ n/a 240 1
1368.4.q $$\chi_{1368}(457, \cdot)$$ n/a 324 2
1368.4.r $$\chi_{1368}(49, \cdot)$$ n/a 360 2
1368.4.s $$\chi_{1368}(505, \cdot)$$ n/a 150 2
1368.4.t $$\chi_{1368}(121, \cdot)$$ n/a 360 2
1368.4.w $$\chi_{1368}(277, \cdot)$$ n/a 1432 2
1368.4.x $$\chi_{1368}(65, \cdot)$$ n/a 360 2
1368.4.y $$\chi_{1368}(331, \cdot)$$ n/a 1432 2
1368.4.z $$\chi_{1368}(311, \cdot)$$ None 0 2
1368.4.be $$\chi_{1368}(487, \cdot)$$ None 0 2
1368.4.bf $$\chi_{1368}(467, \cdot)$$ n/a 480 2
1368.4.bi $$\chi_{1368}(797, \cdot)$$ n/a 1432 2
1368.4.bl $$\chi_{1368}(293, \cdot)$$ n/a 1432 2
1368.4.bm $$\chi_{1368}(103, \cdot)$$ None 0 2
1368.4.bn $$\chi_{1368}(83, \cdot)$$ n/a 1432 2
1368.4.bq $$\chi_{1368}(419, \cdot)$$ n/a 1296 2
1368.4.br $$\chi_{1368}(151, \cdot)$$ None 0 2
1368.4.bu $$\chi_{1368}(1133, \cdot)$$ n/a 480 2
1368.4.bx $$\chi_{1368}(1171, \cdot)$$ n/a 596 2
1368.4.by $$\chi_{1368}(1151, \cdot)$$ None 0 2
1368.4.cb $$\chi_{1368}(349, \cdot)$$ n/a 1432 2
1368.4.cc $$\chi_{1368}(977, \cdot)$$ n/a 360 2
1368.4.cf $$\chi_{1368}(113, \cdot)$$ n/a 360 2
1368.4.cg $$\chi_{1368}(229, \cdot)$$ n/a 1296 2
1368.4.cl $$\chi_{1368}(191, \cdot)$$ None 0 2
1368.4.cm $$\chi_{1368}(835, \cdot)$$ n/a 1432 2
1368.4.cp $$\chi_{1368}(259, \cdot)$$ n/a 1432 2
1368.4.cq $$\chi_{1368}(239, \cdot)$$ None 0 2
1368.4.ct $$\chi_{1368}(1189, \cdot)$$ n/a 596 2
1368.4.cu $$\chi_{1368}(449, \cdot)$$ n/a 120 2
1368.4.cv $$\chi_{1368}(221, \cdot)$$ n/a 1432 2
1368.4.da $$\chi_{1368}(31, \cdot)$$ None 0 2
1368.4.db $$\chi_{1368}(11, \cdot)$$ n/a 1432 2
1368.4.dc $$\chi_{1368}(73, \cdot)$$ n/a 450 6
1368.4.dd $$\chi_{1368}(25, \cdot)$$ n/a 1080 6
1368.4.de $$\chi_{1368}(169, \cdot)$$ n/a 1080 6
1368.4.dg $$\chi_{1368}(67, \cdot)$$ n/a 4296 6
1368.4.di $$\chi_{1368}(23, \cdot)$$ None 0 6
1368.4.dj $$\chi_{1368}(79, \cdot)$$ None 0 6
1368.4.dl $$\chi_{1368}(275, \cdot)$$ n/a 4296 6
1368.4.dn $$\chi_{1368}(41, \cdot)$$ n/a 1080 6
1368.4.dp $$\chi_{1368}(61, \cdot)$$ n/a 4296 6
1368.4.dt $$\chi_{1368}(53, \cdot)$$ n/a 1440 6
1368.4.du $$\chi_{1368}(253, \cdot)$$ n/a 1788 6
1368.4.dw $$\chi_{1368}(89, \cdot)$$ n/a 360 6
1368.4.dz $$\chi_{1368}(29, \cdot)$$ n/a 4296 6
1368.4.eb $$\chi_{1368}(131, \cdot)$$ n/a 4296 6
1368.4.ed $$\chi_{1368}(295, \cdot)$$ None 0 6
1368.4.eg $$\chi_{1368}(91, \cdot)$$ n/a 1788 6
1368.4.ei $$\chi_{1368}(215, \cdot)$$ None 0 6
1368.4.ej $$\chi_{1368}(127, \cdot)$$ None 0 6
1368.4.el $$\chi_{1368}(35, \cdot)$$ n/a 1440 6
1368.4.eo $$\chi_{1368}(47, \cdot)$$ None 0 6
1368.4.eq $$\chi_{1368}(211, \cdot)$$ n/a 4296 6
1368.4.et $$\chi_{1368}(173, \cdot)$$ n/a 4296 6
1368.4.eu $$\chi_{1368}(85, \cdot)$$ n/a 4296 6
1368.4.ew $$\chi_{1368}(257, \cdot)$$ n/a 1080 6

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1368))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1368)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(684))$$$$^{\oplus 2}$$