# Properties

 Label 1368.2 Level 1368 Weight 2 Dimension 22651 Nonzero newspaces 48 Sturm bound 207360 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$1368 = 2^{3} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$207360$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1368))$$.

Total New Old
Modular forms 53568 23263 30305
Cusp forms 50113 22651 27462
Eisenstein series 3455 612 2843

## Trace form

 $$22651 q - 50 q^{2} - 66 q^{3} - 50 q^{4} - 8 q^{5} - 56 q^{6} - 50 q^{7} - 26 q^{8} - 126 q^{9} + O(q^{10})$$ $$22651 q - 50 q^{2} - 66 q^{3} - 50 q^{4} - 8 q^{5} - 56 q^{6} - 50 q^{7} - 26 q^{8} - 126 q^{9} - 114 q^{10} - 20 q^{11} - 44 q^{12} + 4 q^{13} - 26 q^{14} - 24 q^{15} - 34 q^{16} - 68 q^{17} - 72 q^{18} - 140 q^{19} - 128 q^{20} + 24 q^{21} - 82 q^{22} - 18 q^{23} - 120 q^{24} - 92 q^{25} - 110 q^{26} - 72 q^{27} - 178 q^{28} - 30 q^{29} - 164 q^{30} - 40 q^{31} - 130 q^{32} - 130 q^{33} - 26 q^{34} - 162 q^{35} - 172 q^{36} - 30 q^{37} - 92 q^{38} - 216 q^{39} - 74 q^{40} - 116 q^{41} - 172 q^{42} - 140 q^{43} - 138 q^{44} - 4 q^{45} - 194 q^{46} - 156 q^{47} - 112 q^{48} - 22 q^{49} - 110 q^{50} - 90 q^{51} - 2 q^{52} + 28 q^{53} - 48 q^{54} - 130 q^{55} + 10 q^{56} - 115 q^{57} - 88 q^{58} - 56 q^{59} + 60 q^{60} + 34 q^{61} + 164 q^{62} - 136 q^{63} + 22 q^{64} + 14 q^{65} + 136 q^{66} + 104 q^{67} + 240 q^{68} - 44 q^{69} + 254 q^{70} - 16 q^{71} + 132 q^{72} - 195 q^{73} + 310 q^{74} - 170 q^{75} + 160 q^{76} + 30 q^{77} + 76 q^{78} + 80 q^{79} + 282 q^{80} - 166 q^{81} + 68 q^{82} - 64 q^{83} + 56 q^{84} - 16 q^{85} + 172 q^{86} - 108 q^{87} + 62 q^{88} - 98 q^{89} - 44 q^{90} - 138 q^{91} - 72 q^{92} + 20 q^{93} - 66 q^{94} - 10 q^{95} - 240 q^{96} - 102 q^{97} - 246 q^{98} - 6 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1368))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1368.2.a $$\chi_{1368}(1, \cdot)$$ 1368.2.a.a 1 1
1368.2.a.b 1
1368.2.a.c 1
1368.2.a.d 1
1368.2.a.e 1
1368.2.a.f 1
1368.2.a.g 1
1368.2.a.h 1
1368.2.a.i 1
1368.2.a.j 1
1368.2.a.k 2
1368.2.a.l 2
1368.2.a.m 3
1368.2.a.n 3
1368.2.a.o 3
1368.2.d $$\chi_{1368}(647, \cdot)$$ None 0 1
1368.2.e $$\chi_{1368}(379, \cdot)$$ 1368.2.e.a 2 1
1368.2.e.b 4
1368.2.e.c 8
1368.2.e.d 8
1368.2.e.e 12
1368.2.e.f 24
1368.2.e.g 40
1368.2.f $$\chi_{1368}(1025, \cdot)$$ 1368.2.f.a 2 1
1368.2.f.b 2
1368.2.f.c 8
1368.2.f.d 8
1368.2.g $$\chi_{1368}(685, \cdot)$$ 1368.2.g.a 2 1
1368.2.g.b 16
1368.2.g.c 18
1368.2.g.d 18
1368.2.g.e 36
1368.2.j $$\chi_{1368}(1331, \cdot)$$ 1368.2.j.a 4 1
1368.2.j.b 4
1368.2.j.c 28
1368.2.j.d 36
1368.2.k $$\chi_{1368}(1063, \cdot)$$ None 0 1
1368.2.p $$\chi_{1368}(341, \cdot)$$ 1368.2.p.a 80 1
1368.2.q $$\chi_{1368}(457, \cdot)$$ n/a 108 2
1368.2.r $$\chi_{1368}(49, \cdot)$$ n/a 120 2
1368.2.s $$\chi_{1368}(505, \cdot)$$ 1368.2.s.a 2 2
1368.2.s.b 2
1368.2.s.c 2
1368.2.s.d 2
1368.2.s.e 2
1368.2.s.f 2
1368.2.s.g 2
1368.2.s.h 4
1368.2.s.i 4
1368.2.s.j 6
1368.2.s.k 6
1368.2.s.l 8
1368.2.s.m 8
1368.2.t $$\chi_{1368}(121, \cdot)$$ n/a 120 2
1368.2.w $$\chi_{1368}(277, \cdot)$$ n/a 472 2
1368.2.x $$\chi_{1368}(65, \cdot)$$ n/a 120 2
1368.2.y $$\chi_{1368}(331, \cdot)$$ n/a 472 2
1368.2.z $$\chi_{1368}(311, \cdot)$$ None 0 2
1368.2.be $$\chi_{1368}(487, \cdot)$$ None 0 2
1368.2.bf $$\chi_{1368}(467, \cdot)$$ n/a 160 2
1368.2.bi $$\chi_{1368}(797, \cdot)$$ n/a 472 2
1368.2.bl $$\chi_{1368}(293, \cdot)$$ n/a 472 2
1368.2.bm $$\chi_{1368}(103, \cdot)$$ None 0 2
1368.2.bn $$\chi_{1368}(83, \cdot)$$ n/a 472 2
1368.2.bq $$\chi_{1368}(419, \cdot)$$ n/a 432 2
1368.2.br $$\chi_{1368}(151, \cdot)$$ None 0 2
1368.2.bu $$\chi_{1368}(1133, \cdot)$$ n/a 160 2
1368.2.bx $$\chi_{1368}(1171, \cdot)$$ n/a 196 2
1368.2.by $$\chi_{1368}(1151, \cdot)$$ None 0 2
1368.2.cb $$\chi_{1368}(349, \cdot)$$ n/a 472 2
1368.2.cc $$\chi_{1368}(977, \cdot)$$ n/a 120 2
1368.2.cf $$\chi_{1368}(113, \cdot)$$ n/a 120 2
1368.2.cg $$\chi_{1368}(229, \cdot)$$ n/a 432 2
1368.2.cl $$\chi_{1368}(191, \cdot)$$ None 0 2
1368.2.cm $$\chi_{1368}(835, \cdot)$$ n/a 472 2
1368.2.cp $$\chi_{1368}(259, \cdot)$$ n/a 472 2
1368.2.cq $$\chi_{1368}(239, \cdot)$$ None 0 2
1368.2.ct $$\chi_{1368}(1189, \cdot)$$ n/a 196 2
1368.2.cu $$\chi_{1368}(449, \cdot)$$ 1368.2.cu.a 20 2
1368.2.cu.b 20
1368.2.cv $$\chi_{1368}(221, \cdot)$$ n/a 472 2
1368.2.da $$\chi_{1368}(31, \cdot)$$ None 0 2
1368.2.db $$\chi_{1368}(11, \cdot)$$ n/a 472 2
1368.2.dc $$\chi_{1368}(73, \cdot)$$ n/a 150 6
1368.2.dd $$\chi_{1368}(25, \cdot)$$ n/a 360 6
1368.2.de $$\chi_{1368}(169, \cdot)$$ n/a 360 6
1368.2.dg $$\chi_{1368}(67, \cdot)$$ n/a 1416 6
1368.2.di $$\chi_{1368}(23, \cdot)$$ None 0 6
1368.2.dj $$\chi_{1368}(79, \cdot)$$ None 0 6
1368.2.dl $$\chi_{1368}(275, \cdot)$$ n/a 1416 6
1368.2.dn $$\chi_{1368}(41, \cdot)$$ n/a 360 6
1368.2.dp $$\chi_{1368}(61, \cdot)$$ n/a 1416 6
1368.2.dt $$\chi_{1368}(53, \cdot)$$ n/a 480 6
1368.2.du $$\chi_{1368}(253, \cdot)$$ n/a 588 6
1368.2.dw $$\chi_{1368}(89, \cdot)$$ n/a 120 6
1368.2.dz $$\chi_{1368}(29, \cdot)$$ n/a 1416 6
1368.2.eb $$\chi_{1368}(131, \cdot)$$ n/a 1416 6
1368.2.ed $$\chi_{1368}(295, \cdot)$$ None 0 6
1368.2.eg $$\chi_{1368}(91, \cdot)$$ n/a 588 6
1368.2.ei $$\chi_{1368}(215, \cdot)$$ None 0 6
1368.2.ej $$\chi_{1368}(127, \cdot)$$ None 0 6
1368.2.el $$\chi_{1368}(35, \cdot)$$ n/a 480 6
1368.2.eo $$\chi_{1368}(47, \cdot)$$ None 0 6
1368.2.eq $$\chi_{1368}(211, \cdot)$$ n/a 1416 6
1368.2.et $$\chi_{1368}(173, \cdot)$$ n/a 1416 6
1368.2.eu $$\chi_{1368}(85, \cdot)$$ n/a 1416 6
1368.2.ew $$\chi_{1368}(257, \cdot)$$ n/a 360 6

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1368))$$ into lower level spaces

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