# Properties

 Label 1872.1 Level 1872 Weight 1 Dimension 61 Nonzero newspaces 12 Newform subspaces 20 Sturm bound 193536 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$1872 = 2^{4} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$12$$ Newform subspaces: $$20$$ Sturm bound: $$193536$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1872))$$.

Total New Old
Modular forms 3080 507 2573
Cusp forms 392 61 331
Eisenstein series 2688 446 2242

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 49 0 12 0

## Trace form

 $$61q - q^{3} + 2q^{5} + 4q^{7} - 7q^{9} + O(q^{10})$$ $$61q - q^{3} + 2q^{5} + 4q^{7} - 7q^{9} + 2q^{11} + 7q^{13} + 2q^{15} + 7q^{17} + 4q^{19} + 4q^{21} - 8q^{22} + 3q^{23} + 2q^{25} + 2q^{27} + 7q^{29} - 2q^{31} + 4q^{33} - 5q^{37} - q^{39} - 3q^{41} - q^{43} - 4q^{45} - 4q^{47} + 11q^{49} - 3q^{51} + 8q^{52} - 4q^{53} - 12q^{55} + 2q^{57} - 2q^{59} - 16q^{61} + 2q^{63} - q^{65} + 8q^{67} - 9q^{69} + 8q^{73} - 2q^{75} + 5q^{79} - 7q^{81} - 5q^{85} + 8q^{88} - 4q^{89} - 6q^{91} + 2q^{93} + 10q^{97} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1872))$$

We only show spaces with odd 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
1872.1.b $$\chi_{1872}(233, \cdot)$$ None 0 1
1872.1.e $$\chi_{1872}(1639, \cdot)$$ None 0 1
1872.1.f $$\chi_{1872}(1457, \cdot)$$ None 0 1
1872.1.i $$\chi_{1872}(415, \cdot)$$ 1872.1.i.a 1 1
1872.1.i.b 1
1872.1.i.c 1
1872.1.k $$\chi_{1872}(703, \cdot)$$ None 0 1
1872.1.l $$\chi_{1872}(1169, \cdot)$$ None 0 1
1872.1.o $$\chi_{1872}(1351, \cdot)$$ None 0 1
1872.1.p $$\chi_{1872}(521, \cdot)$$ None 0 1
1872.1.v $$\chi_{1872}(395, \cdot)$$ None 0 2
1872.1.w $$\chi_{1872}(109, \cdot)$$ None 0 2
1872.1.z $$\chi_{1872}(53, \cdot)$$ None 0 2
1872.1.bb $$\chi_{1872}(883, \cdot)$$ 1872.1.bb.a 8 2
1872.1.bc $$\chi_{1872}(73, \cdot)$$ None 0 2
1872.1.bd $$\chi_{1872}(577, \cdot)$$ 1872.1.bd.a 2 2
1872.1.bg $$\chi_{1872}(863, \cdot)$$ 1872.1.bg.a 4 2
1872.1.bh $$\chi_{1872}(359, \cdot)$$ None 0 2
1872.1.bl $$\chi_{1872}(701, \cdot)$$ None 0 2
1872.1.bn $$\chi_{1872}(235, \cdot)$$ None 0 2
1872.1.bo $$\chi_{1872}(541, \cdot)$$ None 0 2
1872.1.br $$\chi_{1872}(827, \cdot)$$ None 0 2
1872.1.bs $$\chi_{1872}(127, \cdot)$$ 1872.1.bs.a 2 2
1872.1.bs.b 2
1872.1.bs.c 2
1872.1.bv $$\chi_{1872}(737, \cdot)$$ 1872.1.bv.a 4 2
1872.1.bw $$\chi_{1872}(55, \cdot)$$ None 0 2
1872.1.bz $$\chi_{1872}(953, \cdot)$$ None 0 2
1872.1.cb $$\chi_{1872}(257, \cdot)$$ None 0 2
1872.1.cc $$\chi_{1872}(1231, \cdot)$$ None 0 2
1872.1.ce $$\chi_{1872}(439, \cdot)$$ None 0 2
1872.1.cg $$\chi_{1872}(1145, \cdot)$$ None 0 2
1872.1.ci $$\chi_{1872}(103, \cdot)$$ None 0 2
1872.1.cj $$\chi_{1872}(1049, \cdot)$$ None 0 2
1872.1.ck $$\chi_{1872}(367, \cdot)$$ None 0 2
1872.1.cm $$\chi_{1872}(545, \cdot)$$ 1872.1.cm.a 2 2
1872.1.cp $$\chi_{1872}(79, \cdot)$$ None 0 2
1872.1.cr $$\chi_{1872}(1265, \cdot)$$ None 0 2
1872.1.cs $$\chi_{1872}(185, \cdot)$$ None 0 2
1872.1.ct $$\chi_{1872}(1447, \cdot)$$ None 0 2
1872.1.cv $$\chi_{1872}(295, \cdot)$$ None 0 2
1872.1.cy $$\chi_{1872}(1193, \cdot)$$ None 0 2
1872.1.da $$\chi_{1872}(113, \cdot)$$ None 0 2
1872.1.dc $$\chi_{1872}(1039, \cdot)$$ 1872.1.dc.a 2 2
1872.1.dc.b 2
1872.1.dd $$\chi_{1872}(209, \cdot)$$ None 0 2
1872.1.df $$\chi_{1872}(1375, \cdot)$$ None 0 2
1872.1.di $$\chi_{1872}(329, \cdot)$$ None 0 2
1872.1.dk $$\chi_{1872}(391, \cdot)$$ None 0 2
1872.1.dl $$\chi_{1872}(857, \cdot)$$ None 0 2
1872.1.dn $$\chi_{1872}(1303, \cdot)$$ None 0 2
1872.1.dp $$\chi_{1872}(511, \cdot)$$ None 0 2
1872.1.ds $$\chi_{1872}(1121, \cdot)$$ None 0 2
1872.1.dt $$\chi_{1872}(809, \cdot)$$ None 0 2
1872.1.du $$\chi_{1872}(199, \cdot)$$ None 0 2
1872.1.dx $$\chi_{1872}(17, \cdot)$$ None 0 2
1872.1.dy $$\chi_{1872}(991, \cdot)$$ 1872.1.dy.a 2 2
1872.1.dy.b 2
1872.1.dy.c 4
1872.1.eb $$\chi_{1872}(37, \cdot)$$ None 0 4
1872.1.ec $$\chi_{1872}(323, \cdot)$$ None 0 4
1872.1.ef $$\chi_{1872}(349, \cdot)$$ None 0 4
1872.1.eh $$\chi_{1872}(227, \cdot)$$ None 0 4
1872.1.ej $$\chi_{1872}(83, \cdot)$$ None 0 4
1872.1.ek $$\chi_{1872}(421, \cdot)$$ None 0 4
1872.1.em $$\chi_{1872}(565, \cdot)$$ None 0 4
1872.1.eo $$\chi_{1872}(11, \cdot)$$ None 0 4
1872.1.er $$\chi_{1872}(43, \cdot)$$ None 0 4
1872.1.et $$\chi_{1872}(653, \cdot)$$ None 0 4
1872.1.eu $$\chi_{1872}(77, \cdot)$$ None 0 4
1872.1.ew $$\chi_{1872}(451, \cdot)$$ None 0 4
1872.1.ex $$\chi_{1872}(139, \cdot)$$ None 0 4
1872.1.fa $$\chi_{1872}(413, \cdot)$$ None 0 4
1872.1.fb $$\chi_{1872}(101, \cdot)$$ None 0 4
1872.1.fe $$\chi_{1872}(547, \cdot)$$ None 0 4
1872.1.fi $$\chi_{1872}(385, \cdot)$$ 1872.1.fi.a 4 4
1872.1.fi.b 4
1872.1.fj $$\chi_{1872}(265, \cdot)$$ None 0 4
1872.1.fk $$\chi_{1872}(167, \cdot)$$ None 0 4
1872.1.fl $$\chi_{1872}(1103, \cdot)$$ None 0 4
1872.1.fq $$\chi_{1872}(71, \cdot)$$ None 0 4
1872.1.fr $$\chi_{1872}(431, \cdot)$$ 1872.1.fr.a 8 4
1872.1.fs $$\chi_{1872}(383, \cdot)$$ None 0 4
1872.1.ft $$\chi_{1872}(119, \cdot)$$ None 0 4
1872.1.fw $$\chi_{1872}(97, \cdot)$$ None 0 4
1872.1.fx $$\chi_{1872}(1033, \cdot)$$ None 0 4
1872.1.gc $$\chi_{1872}(145, \cdot)$$ 1872.1.gc.a 4 4
1872.1.gd $$\chi_{1872}(505, \cdot)$$ None 0 4
1872.1.ge $$\chi_{1872}(409, \cdot)$$ None 0 4
1872.1.gf $$\chi_{1872}(817, \cdot)$$ None 0 4
1872.1.gk $$\chi_{1872}(551, \cdot)$$ None 0 4
1872.1.gl $$\chi_{1872}(47, \cdot)$$ None 0 4
1872.1.gm $$\chi_{1872}(365, \cdot)$$ None 0 4
1872.1.go $$\chi_{1872}(595, \cdot)$$ None 0 4
1872.1.gp $$\chi_{1872}(355, \cdot)$$ None 0 4
1872.1.gs $$\chi_{1872}(269, \cdot)$$ None 0 4
1872.1.gt $$\chi_{1872}(29, \cdot)$$ None 0 4
1872.1.gw $$\chi_{1872}(259, \cdot)$$ None 0 4
1872.1.gz $$\chi_{1872}(211, \cdot)$$ None 0 4
1872.1.hb $$\chi_{1872}(173, \cdot)$$ None 0 4
1872.1.hc $$\chi_{1872}(587, \cdot)$$ None 0 4
1872.1.he $$\chi_{1872}(229, \cdot)$$ None 0 4
1872.1.hg $$\chi_{1872}(301, \cdot)$$ None 0 4
1872.1.hj $$\chi_{1872}(371, \cdot)$$ None 0 4
1872.1.hl $$\chi_{1872}(515, \cdot)$$ None 0 4
1872.1.hn $$\chi_{1872}(85, \cdot)$$ None 0 4
1872.1.ho $$\chi_{1872}(683, \cdot)$$ None 0 4
1872.1.hr $$\chi_{1872}(397, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1872))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1872)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 9}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(468))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(936))$$$$^{\oplus 2}$$