# Properties

 Label 1872.2 Level 1872 Weight 2 Dimension 42134 Nonzero newspaces 70 Sturm bound 387072 Trace bound 77

## Defining parameters

 Level: $$N$$ = $$1872 = 2^{4} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$70$$ Sturm bound: $$387072$$ Trace bound: $$77$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1872))$$.

Total New Old
Modular forms 99456 43024 56432
Cusp forms 94081 42134 51947
Eisenstein series 5375 890 4485

## Trace form

 $$42134 q - 60 q^{2} - 60 q^{3} - 64 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 72 q^{8} - 28 q^{9} + O(q^{10})$$ $$42134 q - 60 q^{2} - 60 q^{3} - 64 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 72 q^{8} - 28 q^{9} - 184 q^{10} - 72 q^{11} - 80 q^{12} - 91 q^{13} - 96 q^{14} - 66 q^{15} - 16 q^{16} - 118 q^{17} - 40 q^{18} - 142 q^{19} + 40 q^{20} - 74 q^{21} + 32 q^{22} - 4 q^{23} - 16 q^{24} + 32 q^{25} - 8 q^{26} - 96 q^{27} - 104 q^{28} - 16 q^{29} - 40 q^{30} - 20 q^{31} - 138 q^{33} - 40 q^{34} + 102 q^{35} - 72 q^{36} - 242 q^{37} - 152 q^{38} - 9 q^{39} - 248 q^{40} - 12 q^{41} - 160 q^{42} + 24 q^{43} - 232 q^{44} - 54 q^{45} - 304 q^{46} + 60 q^{47} - 184 q^{48} - 250 q^{49} - 228 q^{50} + 4 q^{51} - 128 q^{52} - 196 q^{53} - 168 q^{54} - 78 q^{55} - 264 q^{56} - 64 q^{57} - 136 q^{58} - 32 q^{59} - 296 q^{60} - 88 q^{61} - 264 q^{62} - 66 q^{63} - 40 q^{64} - 267 q^{65} - 416 q^{66} - 80 q^{67} - 232 q^{68} - 250 q^{69} + 16 q^{70} - 182 q^{71} - 304 q^{72} - 14 q^{73} - 176 q^{74} - 164 q^{75} + 8 q^{76} - 146 q^{77} - 196 q^{78} - 190 q^{79} - 328 q^{80} - 332 q^{81} - 200 q^{82} - 252 q^{83} - 368 q^{84} + 10 q^{85} - 256 q^{86} - 198 q^{87} - 88 q^{88} + 42 q^{89} - 368 q^{90} - 184 q^{91} - 184 q^{92} - 18 q^{93} - 64 q^{94} - 194 q^{95} - 216 q^{96} - 16 q^{97} - 28 q^{98} - 90 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1872))$$

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
1872.2.a $$\chi_{1872}(1, \cdot)$$ 1872.2.a.a 1 1
1872.2.a.b 1
1872.2.a.c 1
1872.2.a.d 1
1872.2.a.e 1
1872.2.a.f 1
1872.2.a.g 1
1872.2.a.h 1
1872.2.a.i 1
1872.2.a.j 1
1872.2.a.k 1
1872.2.a.l 1
1872.2.a.m 1
1872.2.a.n 1
1872.2.a.o 1
1872.2.a.p 1
1872.2.a.q 1
1872.2.a.r 1
1872.2.a.s 1
1872.2.a.t 1
1872.2.a.u 2
1872.2.a.v 2
1872.2.a.w 2
1872.2.a.x 2
1872.2.a.y 2
1872.2.c $$\chi_{1872}(1585, \cdot)$$ 1872.2.c.a 2 1
1872.2.c.b 2
1872.2.c.c 2
1872.2.c.d 2
1872.2.c.e 2
1872.2.c.f 2
1872.2.c.g 2
1872.2.c.h 2
1872.2.c.i 2
1872.2.c.j 4
1872.2.c.k 4
1872.2.c.l 8
1872.2.d $$\chi_{1872}(287, \cdot)$$ 1872.2.d.a 4 1
1872.2.d.b 4
1872.2.d.c 8
1872.2.d.d 8
1872.2.g $$\chi_{1872}(937, \cdot)$$ None 0 1
1872.2.h $$\chi_{1872}(935, \cdot)$$ None 0 1
1872.2.j $$\chi_{1872}(1223, \cdot)$$ None 0 1
1872.2.m $$\chi_{1872}(649, \cdot)$$ None 0 1
1872.2.n $$\chi_{1872}(1871, \cdot)$$ 1872.2.n.a 4 1
1872.2.n.b 4
1872.2.n.c 4
1872.2.n.d 8
1872.2.n.e 8
1872.2.q $$\chi_{1872}(625, \cdot)$$ n/a 144 2
1872.2.r $$\chi_{1872}(1537, \cdot)$$ n/a 164 2
1872.2.s $$\chi_{1872}(529, \cdot)$$ n/a 164 2
1872.2.t $$\chi_{1872}(289, \cdot)$$ 1872.2.t.a 2 2
1872.2.t.b 2
1872.2.t.c 2
1872.2.t.d 2
1872.2.t.e 2
1872.2.t.f 2
1872.2.t.g 2
1872.2.t.h 2
1872.2.t.i 2
1872.2.t.j 2
1872.2.t.k 2
1872.2.t.l 2
1872.2.t.m 2
1872.2.t.n 4
1872.2.t.o 4
1872.2.t.p 4
1872.2.t.q 4
1872.2.t.r 4
1872.2.t.s 4
1872.2.t.t 6
1872.2.t.u 6
1872.2.t.v 6
1872.2.u $$\chi_{1872}(1243, \cdot)$$ n/a 276 2
1872.2.x $$\chi_{1872}(125, \cdot)$$ n/a 224 2
1872.2.y $$\chi_{1872}(467, \cdot)$$ n/a 224 2
1872.2.ba $$\chi_{1872}(469, \cdot)$$ n/a 240 2
1872.2.be $$\chi_{1872}(343, \cdot)$$ None 0 2
1872.2.bf $$\chi_{1872}(1279, \cdot)$$ 1872.2.bf.a 2 2
1872.2.bf.b 2
1872.2.bf.c 2
1872.2.bf.d 2
1872.2.bf.e 2
1872.2.bf.f 4
1872.2.bf.g 4
1872.2.bf.h 4
1872.2.bf.i 4
1872.2.bf.j 4
1872.2.bf.k 4
1872.2.bf.l 8
1872.2.bf.m 8
1872.2.bf.n 8
1872.2.bf.o 12
1872.2.bi $$\chi_{1872}(161, \cdot)$$ 1872.2.bi.a 4 2
1872.2.bi.b 4
1872.2.bi.c 12
1872.2.bi.d 12
1872.2.bi.e 12
1872.2.bi.f 12
1872.2.bj $$\chi_{1872}(1097, \cdot)$$ None 0 2
1872.2.bk $$\chi_{1872}(755, \cdot)$$ n/a 192 2
1872.2.bm $$\chi_{1872}(181, \cdot)$$ n/a 276 2
1872.2.bp $$\chi_{1872}(1061, \cdot)$$ n/a 224 2
1872.2.bq $$\chi_{1872}(307, \cdot)$$ n/a 276 2
1872.2.bt $$\chi_{1872}(647, \cdot)$$ None 0 2
1872.2.bu $$\chi_{1872}(217, \cdot)$$ None 0 2
1872.2.bx $$\chi_{1872}(575, \cdot)$$ 1872.2.bx.a 8 2
1872.2.bx.b 8
1872.2.bx.c 20
1872.2.bx.d 20
1872.2.by $$\chi_{1872}(433, \cdot)$$ 1872.2.by.a 2 2
1872.2.by.b 2
1872.2.by.c 2
1872.2.by.d 2
1872.2.by.e 2
1872.2.by.f 2
1872.2.by.g 4
1872.2.by.h 4
1872.2.by.i 4
1872.2.by.j 4
1872.2.by.k 4
1872.2.by.l 4
1872.2.by.m 8
1872.2.by.n 8
1872.2.by.o 16
1872.2.ca $$\chi_{1872}(745, \cdot)$$ None 0 2
1872.2.cd $$\chi_{1872}(887, \cdot)$$ None 0 2
1872.2.cf $$\chi_{1872}(95, \cdot)$$ n/a 168 2
1872.2.ch $$\chi_{1872}(623, \cdot)$$ n/a 168 2
1872.2.cl $$\chi_{1872}(263, \cdot)$$ None 0 2
1872.2.cn $$\chi_{1872}(25, \cdot)$$ None 0 2
1872.2.co $$\chi_{1872}(599, \cdot)$$ None 0 2
1872.2.cq $$\chi_{1872}(121, \cdot)$$ None 0 2
1872.2.cu $$\chi_{1872}(959, \cdot)$$ n/a 168 2
1872.2.cw $$\chi_{1872}(191, \cdot)$$ n/a 168 2
1872.2.cx $$\chi_{1872}(49, \cdot)$$ n/a 164 2
1872.2.cz $$\chi_{1872}(601, \cdot)$$ None 0 2
1872.2.db $$\chi_{1872}(311, \cdot)$$ None 0 2
1872.2.de $$\chi_{1872}(313, \cdot)$$ None 0 2
1872.2.dg $$\chi_{1872}(1031, \cdot)$$ None 0 2
1872.2.dh $$\chi_{1872}(673, \cdot)$$ n/a 164 2
1872.2.dj $$\chi_{1872}(911, \cdot)$$ n/a 144 2
1872.2.dm $$\chi_{1872}(337, \cdot)$$ n/a 164 2
1872.2.do $$\chi_{1872}(815, \cdot)$$ n/a 168 2
1872.2.dq $$\chi_{1872}(23, \cdot)$$ None 0 2
1872.2.dr $$\chi_{1872}(1465, \cdot)$$ None 0 2
1872.2.dv $$\chi_{1872}(719, \cdot)$$ 1872.2.dv.a 4 2
1872.2.dv.b 4
1872.2.dv.c 8
1872.2.dv.d 20
1872.2.dv.e 20
1872.2.dw $$\chi_{1872}(361, \cdot)$$ None 0 2
1872.2.dz $$\chi_{1872}(503, \cdot)$$ None 0 2
1872.2.ea $$\chi_{1872}(197, \cdot)$$ n/a 448 4
1872.2.ed $$\chi_{1872}(19, \cdot)$$ n/a 552 4
1872.2.ee $$\chi_{1872}(245, \cdot)$$ n/a 1328 4
1872.2.eg $$\chi_{1872}(187, \cdot)$$ n/a 1328 4
1872.2.ei $$\chi_{1872}(331, \cdot)$$ n/a 1328 4
1872.2.el $$\chi_{1872}(461, \cdot)$$ n/a 1328 4
1872.2.en $$\chi_{1872}(317, \cdot)$$ n/a 1328 4
1872.2.ep $$\chi_{1872}(115, \cdot)$$ n/a 1328 4
1872.2.eq $$\chi_{1872}(61, \cdot)$$ n/a 1328 4
1872.2.es $$\chi_{1872}(491, \cdot)$$ n/a 1328 4
1872.2.ev $$\chi_{1872}(131, \cdot)$$ n/a 1152 4
1872.2.ey $$\chi_{1872}(829, \cdot)$$ n/a 552 4
1872.2.ez $$\chi_{1872}(205, \cdot)$$ n/a 1328 4
1872.2.fc $$\chi_{1872}(35, \cdot)$$ n/a 448 4
1872.2.fd $$\chi_{1872}(347, \cdot)$$ n/a 1328 4
1872.2.ff $$\chi_{1872}(493, \cdot)$$ n/a 1328 4
1872.2.fg $$\chi_{1872}(31, \cdot)$$ n/a 336 4
1872.2.fh $$\chi_{1872}(151, \cdot)$$ None 0 4
1872.2.fm $$\chi_{1872}(89, \cdot)$$ None 0 4
1872.2.fn $$\chi_{1872}(305, \cdot)$$ n/a 112 4
1872.2.fo $$\chi_{1872}(353, \cdot)$$ n/a 328 4
1872.2.fp $$\chi_{1872}(617, \cdot)$$ None 0 4
1872.2.fu $$\chi_{1872}(41, \cdot)$$ None 0 4
1872.2.fv $$\chi_{1872}(401, \cdot)$$ n/a 328 4
1872.2.fy $$\chi_{1872}(271, \cdot)$$ n/a 140 4
1872.2.fz $$\chi_{1872}(487, \cdot)$$ None 0 4
1872.2.ga $$\chi_{1872}(583, \cdot)$$ None 0 4
1872.2.gb $$\chi_{1872}(175, \cdot)$$ n/a 336 4
1872.2.gg $$\chi_{1872}(799, \cdot)$$ n/a 336 4
1872.2.gh $$\chi_{1872}(7, \cdot)$$ None 0 4
1872.2.gi $$\chi_{1872}(281, \cdot)$$ None 0 4
1872.2.gj $$\chi_{1872}(785, \cdot)$$ n/a 328 4
1872.2.gn $$\chi_{1872}(155, \cdot)$$ n/a 1328 4
1872.2.gq $$\chi_{1872}(685, \cdot)$$ n/a 552 4
1872.2.gr $$\chi_{1872}(133, \cdot)$$ n/a 1328 4
1872.2.gu $$\chi_{1872}(179, \cdot)$$ n/a 448 4
1872.2.gv $$\chi_{1872}(563, \cdot)$$ n/a 1328 4
1872.2.gx $$\chi_{1872}(157, \cdot)$$ n/a 1152 4
1872.2.gy $$\chi_{1872}(277, \cdot)$$ n/a 1328 4
1872.2.ha $$\chi_{1872}(419, \cdot)$$ n/a 1328 4
1872.2.hd $$\chi_{1872}(643, \cdot)$$ n/a 1328 4
1872.2.hf $$\chi_{1872}(605, \cdot)$$ n/a 1328 4
1872.2.hh $$\chi_{1872}(5, \cdot)$$ n/a 1328 4
1872.2.hi $$\chi_{1872}(499, \cdot)$$ n/a 1328 4
1872.2.hk $$\chi_{1872}(67, \cdot)$$ n/a 1328 4
1872.2.hm $$\chi_{1872}(149, \cdot)$$ n/a 1328 4
1872.2.hp $$\chi_{1872}(163, \cdot)$$ n/a 552 4
1872.2.hq $$\chi_{1872}(917, \cdot)$$ n/a 448 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1872))$$ into lower level spaces

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