# Properties

 Label 1872.4 Level 1872 Weight 4 Dimension 127292 Nonzero newspaces 70 Sturm bound 774144 Trace bound 77

## Defining parameters

 Level: $$N$$ = $$1872 = 2^{4} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$70$$ Sturm bound: $$774144$$ Trace bound: $$77$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1872))$$.

Total New Old
Modular forms 292992 128182 164810
Cusp forms 287616 127292 160324
Eisenstein series 5376 890 4486

## Trace form

 $$127292 q - 60 q^{2} - 60 q^{3} - 80 q^{4} - 76 q^{5} - 80 q^{6} - 72 q^{7} + 24 q^{8} + 20 q^{9} + O(q^{10})$$ $$127292 q - 60 q^{2} - 60 q^{3} - 80 q^{4} - 76 q^{5} - 80 q^{6} - 72 q^{7} + 24 q^{8} + 20 q^{9} - 48 q^{10} + 96 q^{11} - 80 q^{12} - 33 q^{13} - 384 q^{14} - 18 q^{15} + 432 q^{16} + 70 q^{17} + 200 q^{18} - 406 q^{19} - 904 q^{20} - 698 q^{21} - 904 q^{22} - 692 q^{23} - 1552 q^{24} - 1374 q^{25} - 892 q^{26} + 624 q^{27} - 1032 q^{28} + 484 q^{29} + 920 q^{30} - 276 q^{31} + 1920 q^{32} - 90 q^{33} + 1848 q^{34} + 1062 q^{35} - 1608 q^{36} + 1650 q^{37} - 2416 q^{38} + 159 q^{39} + 1384 q^{40} - 1200 q^{41} + 1280 q^{42} - 4016 q^{43} + 4360 q^{44} + 426 q^{45} + 3440 q^{46} - 6564 q^{47} + 4808 q^{48} - 956 q^{49} + 7140 q^{50} - 3980 q^{51} + 1896 q^{52} + 3424 q^{53} + 360 q^{54} + 6658 q^{55} - 5832 q^{56} - 2320 q^{57} - 4592 q^{58} + 8456 q^{59} - 15944 q^{60} - 108 q^{61} - 9528 q^{62} + 5022 q^{63} - 3368 q^{64} - 1407 q^{65} + 9664 q^{66} - 8008 q^{67} + 6808 q^{68} + 5606 q^{69} - 7008 q^{70} - 3622 q^{71} + 15824 q^{72} - 11778 q^{73} + 8120 q^{74} + 988 q^{75} - 2504 q^{76} + 10574 q^{77} + 428 q^{78} + 2210 q^{79} - 13448 q^{80} + 772 q^{81} - 7080 q^{82} + 2988 q^{83} - 19184 q^{84} + 16306 q^{85} + 1816 q^{86} + 426 q^{87} + 25992 q^{88} + 8646 q^{89} - 2384 q^{90} + 7752 q^{91} + 29032 q^{92} - 1842 q^{93} + 21664 q^{94} + 830 q^{95} + 12840 q^{96} - 11108 q^{97} + 13108 q^{98} + 3078 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1872))$$

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
1872.4.a $$\chi_{1872}(1, \cdot)$$ 1872.4.a.a 1 1
1872.4.a.b 1
1872.4.a.c 1
1872.4.a.d 1
1872.4.a.e 1
1872.4.a.f 1
1872.4.a.g 1
1872.4.a.h 1
1872.4.a.i 1
1872.4.a.j 1
1872.4.a.k 1
1872.4.a.l 1
1872.4.a.m 1
1872.4.a.n 1
1872.4.a.o 1
1872.4.a.p 1
1872.4.a.q 1
1872.4.a.r 1
1872.4.a.s 2
1872.4.a.t 2
1872.4.a.u 2
1872.4.a.v 2
1872.4.a.w 2
1872.4.a.x 2
1872.4.a.y 2
1872.4.a.z 2
1872.4.a.ba 2
1872.4.a.bb 2
1872.4.a.bc 2
1872.4.a.bd 2
1872.4.a.be 2
1872.4.a.bf 2
1872.4.a.bg 2
1872.4.a.bh 2
1872.4.a.bi 2
1872.4.a.bj 3
1872.4.a.bk 3
1872.4.a.bl 3
1872.4.a.bm 3
1872.4.a.bn 4
1872.4.a.bo 4
1872.4.a.bp 4
1872.4.a.bq 4
1872.4.a.br 5
1872.4.a.bs 5
1872.4.c $$\chi_{1872}(1585, \cdot)$$ n/a 104 1
1872.4.d $$\chi_{1872}(287, \cdot)$$ 1872.4.d.a 12 1
1872.4.d.b 12
1872.4.d.c 24
1872.4.d.d 24
1872.4.g $$\chi_{1872}(937, \cdot)$$ None 0 1
1872.4.h $$\chi_{1872}(935, \cdot)$$ None 0 1
1872.4.j $$\chi_{1872}(1223, \cdot)$$ None 0 1
1872.4.m $$\chi_{1872}(649, \cdot)$$ None 0 1
1872.4.n $$\chi_{1872}(1871, \cdot)$$ 1872.4.n.a 4 1
1872.4.n.b 4
1872.4.n.c 4
1872.4.n.d 16
1872.4.n.e 56
1872.4.q $$\chi_{1872}(625, \cdot)$$ n/a 432 2
1872.4.r $$\chi_{1872}(1537, \cdot)$$ n/a 500 2
1872.4.s $$\chi_{1872}(529, \cdot)$$ n/a 500 2
1872.4.t $$\chi_{1872}(289, \cdot)$$ n/a 208 2
1872.4.u $$\chi_{1872}(1243, \cdot)$$ n/a 836 2
1872.4.x $$\chi_{1872}(125, \cdot)$$ n/a 672 2
1872.4.y $$\chi_{1872}(467, \cdot)$$ n/a 672 2
1872.4.ba $$\chi_{1872}(469, \cdot)$$ n/a 720 2
1872.4.be $$\chi_{1872}(343, \cdot)$$ None 0 2
1872.4.bf $$\chi_{1872}(1279, \cdot)$$ n/a 210 2
1872.4.bi $$\chi_{1872}(161, \cdot)$$ n/a 168 2
1872.4.bj $$\chi_{1872}(1097, \cdot)$$ None 0 2
1872.4.bk $$\chi_{1872}(755, \cdot)$$ n/a 576 2
1872.4.bm $$\chi_{1872}(181, \cdot)$$ n/a 836 2
1872.4.bp $$\chi_{1872}(1061, \cdot)$$ n/a 672 2
1872.4.bq $$\chi_{1872}(307, \cdot)$$ n/a 836 2
1872.4.bt $$\chi_{1872}(647, \cdot)$$ None 0 2
1872.4.bu $$\chi_{1872}(217, \cdot)$$ None 0 2
1872.4.bx $$\chi_{1872}(575, \cdot)$$ n/a 168 2
1872.4.by $$\chi_{1872}(433, \cdot)$$ n/a 208 2
1872.4.ca $$\chi_{1872}(745, \cdot)$$ None 0 2
1872.4.cd $$\chi_{1872}(887, \cdot)$$ None 0 2
1872.4.cf $$\chi_{1872}(95, \cdot)$$ n/a 504 2
1872.4.ch $$\chi_{1872}(623, \cdot)$$ n/a 504 2
1872.4.cl $$\chi_{1872}(263, \cdot)$$ None 0 2
1872.4.cn $$\chi_{1872}(25, \cdot)$$ None 0 2
1872.4.co $$\chi_{1872}(599, \cdot)$$ None 0 2
1872.4.cq $$\chi_{1872}(121, \cdot)$$ None 0 2
1872.4.cu $$\chi_{1872}(959, \cdot)$$ n/a 504 2
1872.4.cw $$\chi_{1872}(191, \cdot)$$ n/a 504 2
1872.4.cx $$\chi_{1872}(49, \cdot)$$ n/a 500 2
1872.4.cz $$\chi_{1872}(601, \cdot)$$ None 0 2
1872.4.db $$\chi_{1872}(311, \cdot)$$ None 0 2
1872.4.de $$\chi_{1872}(313, \cdot)$$ None 0 2
1872.4.dg $$\chi_{1872}(1031, \cdot)$$ None 0 2
1872.4.dh $$\chi_{1872}(673, \cdot)$$ n/a 500 2
1872.4.dj $$\chi_{1872}(911, \cdot)$$ n/a 432 2
1872.4.dm $$\chi_{1872}(337, \cdot)$$ n/a 500 2
1872.4.do $$\chi_{1872}(815, \cdot)$$ n/a 504 2
1872.4.dq $$\chi_{1872}(23, \cdot)$$ None 0 2
1872.4.dr $$\chi_{1872}(1465, \cdot)$$ None 0 2
1872.4.dv $$\chi_{1872}(719, \cdot)$$ n/a 168 2
1872.4.dw $$\chi_{1872}(361, \cdot)$$ None 0 2
1872.4.dz $$\chi_{1872}(503, \cdot)$$ None 0 2
1872.4.ea $$\chi_{1872}(197, \cdot)$$ n/a 1344 4
1872.4.ed $$\chi_{1872}(19, \cdot)$$ n/a 1672 4
1872.4.ee $$\chi_{1872}(245, \cdot)$$ n/a 4016 4
1872.4.eg $$\chi_{1872}(187, \cdot)$$ n/a 4016 4
1872.4.ei $$\chi_{1872}(331, \cdot)$$ n/a 4016 4
1872.4.el $$\chi_{1872}(461, \cdot)$$ n/a 4016 4
1872.4.en $$\chi_{1872}(317, \cdot)$$ n/a 4016 4
1872.4.ep $$\chi_{1872}(115, \cdot)$$ n/a 4016 4
1872.4.eq $$\chi_{1872}(61, \cdot)$$ n/a 4016 4
1872.4.es $$\chi_{1872}(491, \cdot)$$ n/a 4016 4
1872.4.ev $$\chi_{1872}(131, \cdot)$$ n/a 3456 4
1872.4.ey $$\chi_{1872}(829, \cdot)$$ n/a 1672 4
1872.4.ez $$\chi_{1872}(205, \cdot)$$ n/a 4016 4
1872.4.fc $$\chi_{1872}(35, \cdot)$$ n/a 1344 4
1872.4.fd $$\chi_{1872}(347, \cdot)$$ n/a 4016 4
1872.4.ff $$\chi_{1872}(493, \cdot)$$ n/a 4016 4
1872.4.fg $$\chi_{1872}(31, \cdot)$$ n/a 1008 4
1872.4.fh $$\chi_{1872}(151, \cdot)$$ None 0 4
1872.4.fm $$\chi_{1872}(89, \cdot)$$ None 0 4
1872.4.fn $$\chi_{1872}(305, \cdot)$$ n/a 336 4
1872.4.fo $$\chi_{1872}(353, \cdot)$$ n/a 1000 4
1872.4.fp $$\chi_{1872}(617, \cdot)$$ None 0 4
1872.4.fu $$\chi_{1872}(41, \cdot)$$ None 0 4
1872.4.fv $$\chi_{1872}(401, \cdot)$$ n/a 1000 4
1872.4.fy $$\chi_{1872}(271, \cdot)$$ n/a 420 4
1872.4.fz $$\chi_{1872}(487, \cdot)$$ None 0 4
1872.4.ga $$\chi_{1872}(583, \cdot)$$ None 0 4
1872.4.gb $$\chi_{1872}(175, \cdot)$$ n/a 1008 4
1872.4.gg $$\chi_{1872}(799, \cdot)$$ n/a 1008 4
1872.4.gh $$\chi_{1872}(7, \cdot)$$ None 0 4
1872.4.gi $$\chi_{1872}(281, \cdot)$$ None 0 4
1872.4.gj $$\chi_{1872}(785, \cdot)$$ n/a 1000 4
1872.4.gn $$\chi_{1872}(155, \cdot)$$ n/a 4016 4
1872.4.gq $$\chi_{1872}(685, \cdot)$$ n/a 1672 4
1872.4.gr $$\chi_{1872}(133, \cdot)$$ n/a 4016 4
1872.4.gu $$\chi_{1872}(179, \cdot)$$ n/a 1344 4
1872.4.gv $$\chi_{1872}(563, \cdot)$$ n/a 4016 4
1872.4.gx $$\chi_{1872}(157, \cdot)$$ n/a 3456 4
1872.4.gy $$\chi_{1872}(277, \cdot)$$ n/a 4016 4
1872.4.ha $$\chi_{1872}(419, \cdot)$$ n/a 4016 4
1872.4.hd $$\chi_{1872}(643, \cdot)$$ n/a 4016 4
1872.4.hf $$\chi_{1872}(605, \cdot)$$ n/a 4016 4
1872.4.hh $$\chi_{1872}(5, \cdot)$$ n/a 4016 4
1872.4.hi $$\chi_{1872}(499, \cdot)$$ n/a 4016 4
1872.4.hk $$\chi_{1872}(67, \cdot)$$ n/a 4016 4
1872.4.hm $$\chi_{1872}(149, \cdot)$$ n/a 4016 4
1872.4.hp $$\chi_{1872}(163, \cdot)$$ n/a 1672 4
1872.4.hq $$\chi_{1872}(917, \cdot)$$ n/a 1344 4

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1872))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1872)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 30}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 20}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 15}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(936))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1872))$$$$^{\oplus 1}$$