# Properties

 Label 1456.2 Level 1456 Weight 2 Dimension 33866 Nonzero newspaces 70 Sturm bound 258048 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$1456 = 2^{4} \cdot 7 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$70$$ Sturm bound: $$258048$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1456))$$.

Total New Old
Modular forms 66528 34858 31670
Cusp forms 62497 33866 28631
Eisenstein series 4031 992 3039

## Trace form

 $$33866 q - 80 q^{2} - 62 q^{3} - 72 q^{4} - 98 q^{5} - 56 q^{6} - 72 q^{7} - 176 q^{8} - 18 q^{9} + O(q^{10})$$ $$33866 q - 80 q^{2} - 62 q^{3} - 72 q^{4} - 98 q^{5} - 56 q^{6} - 72 q^{7} - 176 q^{8} - 18 q^{9} - 72 q^{10} - 46 q^{11} - 88 q^{12} - 106 q^{13} - 224 q^{14} - 128 q^{15} - 104 q^{16} - 178 q^{17} - 64 q^{18} - 18 q^{19} - 56 q^{20} - 88 q^{21} - 192 q^{22} - 18 q^{23} - 72 q^{24} + 42 q^{25} - 76 q^{26} - 116 q^{27} - 80 q^{28} - 192 q^{29} - 88 q^{30} - 70 q^{31} - 40 q^{32} - 130 q^{33} - 56 q^{34} - 44 q^{35} - 208 q^{36} - 42 q^{37} - 120 q^{38} - 42 q^{39} - 200 q^{40} + 36 q^{41} - 240 q^{42} - 20 q^{43} - 184 q^{44} - 40 q^{45} - 144 q^{46} + 46 q^{47} - 280 q^{48} - 224 q^{49} - 384 q^{50} + 34 q^{51} - 200 q^{52} - 250 q^{53} - 408 q^{54} + 12 q^{55} - 280 q^{56} - 144 q^{57} - 288 q^{58} - 54 q^{59} - 408 q^{60} - 138 q^{61} - 224 q^{62} - 76 q^{63} - 360 q^{64} - 166 q^{65} - 392 q^{66} - 94 q^{67} - 192 q^{68} - 180 q^{69} - 176 q^{70} - 84 q^{71} - 248 q^{72} + 30 q^{73} - 72 q^{74} + 12 q^{75} - 24 q^{76} - 10 q^{77} - 224 q^{78} - 42 q^{79} - 40 q^{80} + 28 q^{81} - 72 q^{82} + 40 q^{83} - 280 q^{84} - 176 q^{85} - 264 q^{86} - 36 q^{87} - 280 q^{88} - 114 q^{89} - 568 q^{90} - 188 q^{91} - 792 q^{92} - 338 q^{93} - 376 q^{94} - 294 q^{95} - 760 q^{96} - 316 q^{97} - 184 q^{98} - 572 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1456))$$

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
1456.2.a $$\chi_{1456}(1, \cdot)$$ 1456.2.a.a 1 1
1456.2.a.b 1
1456.2.a.c 1
1456.2.a.d 1
1456.2.a.e 1
1456.2.a.f 1
1456.2.a.g 1
1456.2.a.h 1
1456.2.a.i 1
1456.2.a.j 1
1456.2.a.k 1
1456.2.a.l 1
1456.2.a.m 1
1456.2.a.n 2
1456.2.a.o 2
1456.2.a.p 2
1456.2.a.q 2
1456.2.a.r 2
1456.2.a.s 2
1456.2.a.t 3
1456.2.a.u 4
1456.2.a.v 4
1456.2.b $$\chi_{1456}(727, \cdot)$$ None 0 1
1456.2.c $$\chi_{1456}(729, \cdot)$$ None 0 1
1456.2.h $$\chi_{1456}(391, \cdot)$$ None 0 1
1456.2.i $$\chi_{1456}(1065, \cdot)$$ None 0 1
1456.2.j $$\chi_{1456}(1119, \cdot)$$ 1456.2.j.a 16 1
1456.2.j.b 32
1456.2.k $$\chi_{1456}(337, \cdot)$$ 1456.2.k.a 2 1
1456.2.k.b 6
1456.2.k.c 6
1456.2.k.d 8
1456.2.k.e 8
1456.2.k.f 12
1456.2.p $$\chi_{1456}(1455, \cdot)$$ 1456.2.p.a 2 1
1456.2.p.b 2
1456.2.p.c 2
1456.2.p.d 2
1456.2.p.e 4
1456.2.p.f 4
1456.2.p.g 8
1456.2.p.h 8
1456.2.p.i 24
1456.2.q $$\chi_{1456}(289, \cdot)$$ n/a 108 2
1456.2.r $$\chi_{1456}(417, \cdot)$$ 1456.2.r.a 2 2
1456.2.r.b 2
1456.2.r.c 2
1456.2.r.d 2
1456.2.r.e 2
1456.2.r.f 2
1456.2.r.g 2
1456.2.r.h 2
1456.2.r.i 2
1456.2.r.j 4
1456.2.r.k 4
1456.2.r.l 6
1456.2.r.m 8
1456.2.r.n 8
1456.2.r.o 8
1456.2.r.p 10
1456.2.r.q 14
1456.2.r.r 16
1456.2.s $$\chi_{1456}(113, \cdot)$$ 1456.2.s.a 2 2
1456.2.s.b 2
1456.2.s.c 2
1456.2.s.d 2
1456.2.s.e 2
1456.2.s.f 2
1456.2.s.g 2
1456.2.s.h 4
1456.2.s.i 4
1456.2.s.j 4
1456.2.s.k 4
1456.2.s.l 4
1456.2.s.m 4
1456.2.s.n 4
1456.2.s.o 4
1456.2.s.p 8
1456.2.s.q 8
1456.2.s.r 8
1456.2.s.s 14
1456.2.t $$\chi_{1456}(81, \cdot)$$ n/a 108 2
1456.2.v $$\chi_{1456}(239, \cdot)$$ 1456.2.v.a 8 2
1456.2.v.b 28
1456.2.v.c 48
1456.2.w $$\chi_{1456}(993, \cdot)$$ n/a 108 2
1456.2.y $$\chi_{1456}(827, \cdot)$$ n/a 336 2
1456.2.z $$\chi_{1456}(125, \cdot)$$ n/a 440 2
1456.2.bd $$\chi_{1456}(27, \cdot)$$ n/a 384 2
1456.2.be $$\chi_{1456}(701, \cdot)$$ n/a 336 2
1456.2.bh $$\chi_{1456}(363, \cdot)$$ n/a 440 2
1456.2.bi $$\chi_{1456}(365, \cdot)$$ n/a 288 2
1456.2.bm $$\chi_{1456}(99, \cdot)$$ n/a 336 2
1456.2.bn $$\chi_{1456}(853, \cdot)$$ n/a 440 2
1456.2.bp $$\chi_{1456}(967, \cdot)$$ None 0 2
1456.2.bq $$\chi_{1456}(265, \cdot)$$ None 0 2
1456.2.bu $$\chi_{1456}(121, \cdot)$$ None 0 2
1456.2.bv $$\chi_{1456}(1095, \cdot)$$ None 0 2
1456.2.bw $$\chi_{1456}(9, \cdot)$$ None 0 2
1456.2.bx $$\chi_{1456}(647, \cdot)$$ None 0 2
1456.2.cc $$\chi_{1456}(225, \cdot)$$ 1456.2.cc.a 4 2
1456.2.cc.b 4
1456.2.cc.c 12
1456.2.cc.d 12
1456.2.cc.e 12
1456.2.cc.f 16
1456.2.cc.g 24
1456.2.cd $$\chi_{1456}(783, \cdot)$$ n/a 112 2
1456.2.ce $$\chi_{1456}(927, \cdot)$$ n/a 112 2
1456.2.cf $$\chi_{1456}(831, \cdot)$$ n/a 112 2
1456.2.co $$\chi_{1456}(753, \cdot)$$ n/a 108 2
1456.2.cp $$\chi_{1456}(495, \cdot)$$ 1456.2.cp.a 32 2
1456.2.cp.b 32
1456.2.cp.c 32
1456.2.cq $$\chi_{1456}(159, \cdot)$$ n/a 112 2
1456.2.cr $$\chi_{1456}(641, \cdot)$$ n/a 108 2
1456.2.cs $$\chi_{1456}(335, \cdot)$$ n/a 112 2
1456.2.cx $$\chi_{1456}(393, \cdot)$$ None 0 2
1456.2.cy $$\chi_{1456}(615, \cdot)$$ None 0 2
1456.2.cz $$\chi_{1456}(25, \cdot)$$ None 0 2
1456.2.da $$\chi_{1456}(1223, \cdot)$$ None 0 2
1456.2.db $$\chi_{1456}(87, \cdot)$$ None 0 2
1456.2.dc $$\chi_{1456}(569, \cdot)$$ None 0 2
1456.2.dl $$\chi_{1456}(199, \cdot)$$ None 0 2
1456.2.dm $$\chi_{1456}(1017, \cdot)$$ None 0 2
1456.2.dn $$\chi_{1456}(1145, \cdot)$$ None 0 2
1456.2.do $$\chi_{1456}(103, \cdot)$$ None 0 2
1456.2.dp $$\chi_{1456}(953, \cdot)$$ None 0 2
1456.2.dq $$\chi_{1456}(55, \cdot)$$ None 0 2
1456.2.dv $$\chi_{1456}(719, \cdot)$$ n/a 112 2
1456.2.dw $$\chi_{1456}(849, \cdot)$$ n/a 108 2
1456.2.dx $$\chi_{1456}(367, \cdot)$$ n/a 112 2
1456.2.eb $$\chi_{1456}(33, \cdot)$$ n/a 216 4
1456.2.ec $$\chi_{1456}(431, \cdot)$$ n/a 224 4
1456.2.ef $$\chi_{1456}(487, \cdot)$$ None 0 4
1456.2.ei $$\chi_{1456}(41, \cdot)$$ None 0 4
1456.2.ej $$\chi_{1456}(73, \cdot)$$ None 0 4
1456.2.ek $$\chi_{1456}(71, \cdot)$$ None 0 4
1456.2.el $$\chi_{1456}(135, \cdot)$$ None 0 4
1456.2.eo $$\chi_{1456}(89, \cdot)$$ None 0 4
1456.2.es $$\chi_{1456}(349, \cdot)$$ n/a 880 4
1456.2.et $$\chi_{1456}(267, \cdot)$$ n/a 672 4
1456.2.ew $$\chi_{1456}(661, \cdot)$$ n/a 880 4
1456.2.ex $$\chi_{1456}(163, \cdot)$$ n/a 880 4
1456.2.ey $$\chi_{1456}(123, \cdot)$$ n/a 880 4
1456.2.ez $$\chi_{1456}(229, \cdot)$$ n/a 880 4
1456.2.fa $$\chi_{1456}(515, \cdot)$$ n/a 880 4
1456.2.fb $$\chi_{1456}(45, \cdot)$$ n/a 880 4
1456.2.fh $$\chi_{1456}(373, \cdot)$$ n/a 880 4
1456.2.fi $$\chi_{1456}(283, \cdot)$$ n/a 880 4
1456.2.fl $$\chi_{1456}(485, \cdot)$$ n/a 880 4
1456.2.fm $$\chi_{1456}(3, \cdot)$$ n/a 880 4
1456.2.fp $$\chi_{1456}(389, \cdot)$$ n/a 880 4
1456.2.fq $$\chi_{1456}(131, \cdot)$$ n/a 768 4
1456.2.ft $$\chi_{1456}(75, \cdot)$$ n/a 880 4
1456.2.fv $$\chi_{1456}(29, \cdot)$$ n/a 672 4
1456.2.fw $$\chi_{1456}(251, \cdot)$$ n/a 880 4
1456.2.fy $$\chi_{1456}(165, \cdot)$$ n/a 880 4
1456.2.gb $$\chi_{1456}(451, \cdot)$$ n/a 880 4
1456.2.gd $$\chi_{1456}(309, \cdot)$$ n/a 672 4
1456.2.ge $$\chi_{1456}(139, \cdot)$$ n/a 880 4
1456.2.gg $$\chi_{1456}(205, \cdot)$$ n/a 880 4
1456.2.gj $$\chi_{1456}(53, \cdot)$$ n/a 768 4
1456.2.gk $$\chi_{1456}(467, \cdot)$$ n/a 880 4
1456.2.gm $$\chi_{1456}(397, \cdot)$$ n/a 880 4
1456.2.gn $$\chi_{1456}(11, \cdot)$$ n/a 880 4
1456.2.gu $$\chi_{1456}(219, \cdot)$$ n/a 880 4
1456.2.gv $$\chi_{1456}(5, \cdot)$$ n/a 880 4
1456.2.gw $$\chi_{1456}(291, \cdot)$$ n/a 880 4
1456.2.gx $$\chi_{1456}(605, \cdot)$$ n/a 880 4
1456.2.gy $$\chi_{1456}(293, \cdot)$$ n/a 880 4
1456.2.gz $$\chi_{1456}(323, \cdot)$$ n/a 672 4
1456.2.hd $$\chi_{1456}(319, \cdot)$$ n/a 224 4
1456.2.hg $$\chi_{1456}(97, \cdot)$$ n/a 216 4
1456.2.hh $$\chi_{1456}(369, \cdot)$$ n/a 216 4
1456.2.hi $$\chi_{1456}(15, \cdot)$$ n/a 168 4
1456.2.hj $$\chi_{1456}(655, \cdot)$$ n/a 224 4
1456.2.hm $$\chi_{1456}(145, \cdot)$$ n/a 216 4
1456.2.hp $$\chi_{1456}(201, \cdot)$$ None 0 4
1456.2.hq $$\chi_{1456}(375, \cdot)$$ None 0 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1456))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1456)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$$$^{\oplus 2}$$