# Properties

 Label 1848.2 Level 1848 Weight 2 Dimension 36280 Nonzero newspaces 48 Sturm bound 368640 Trace bound 12

## Defining parameters

 Level: $$N$$ = $$1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$368640$$ Trace bound: $$12$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1848))$$.

Total New Old
Modular forms 95040 37000 58040
Cusp forms 89281 36280 53001
Eisenstein series 5759 720 5039

## Trace form

 $$36280 q - 8 q^{2} - 40 q^{3} - 72 q^{4} - 8 q^{5} - 20 q^{6} - 84 q^{7} + 16 q^{8} - 80 q^{9} + O(q^{10})$$ $$36280 q - 8 q^{2} - 40 q^{3} - 72 q^{4} - 8 q^{5} - 20 q^{6} - 84 q^{7} + 16 q^{8} - 80 q^{9} - 40 q^{10} - 4 q^{11} - 36 q^{12} - 32 q^{13} + 8 q^{14} - 96 q^{15} - 56 q^{16} - 72 q^{17} - 52 q^{18} - 116 q^{19} + 40 q^{20} - 20 q^{21} - 132 q^{22} + 32 q^{23} - 4 q^{24} - 156 q^{25} + 88 q^{26} + 32 q^{27} + 116 q^{28} - 16 q^{29} + 112 q^{30} + 48 q^{31} + 192 q^{32} + 248 q^{34} + 132 q^{35} + 124 q^{36} + 48 q^{37} + 304 q^{38} + 152 q^{39} + 376 q^{40} + 112 q^{41} + 8 q^{42} - 8 q^{43} + 232 q^{44} + 136 q^{45} + 72 q^{46} + 168 q^{47} + 40 q^{48} - 32 q^{49} + 104 q^{50} + 186 q^{51} - 8 q^{52} + 64 q^{53} - 36 q^{54} + 108 q^{55} - 104 q^{56} + 38 q^{57} - 184 q^{58} + 160 q^{59} - 132 q^{60} - 8 q^{61} - 232 q^{62} + 118 q^{63} - 384 q^{64} + 80 q^{65} - 114 q^{66} + 8 q^{67} - 120 q^{68} + 64 q^{69} - 328 q^{70} + 208 q^{71} - 248 q^{72} - 80 q^{73} - 136 q^{74} + 150 q^{75} - 472 q^{76} + 24 q^{77} - 552 q^{78} + 296 q^{79} - 440 q^{80} - 120 q^{81} - 600 q^{82} + 288 q^{83} - 390 q^{84} + 80 q^{85} - 352 q^{86} - 12 q^{87} - 676 q^{88} - 32 q^{89} - 312 q^{90} - 72 q^{91} - 344 q^{92} - 104 q^{93} - 584 q^{94} + 48 q^{95} - 480 q^{96} + 28 q^{97} - 348 q^{98} - 240 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1848))$$

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
1848.2.a $$\chi_{1848}(1, \cdot)$$ 1848.2.a.a 1 1
1848.2.a.b 1
1848.2.a.c 1
1848.2.a.d 1
1848.2.a.e 1
1848.2.a.f 1
1848.2.a.g 1
1848.2.a.h 1
1848.2.a.i 1
1848.2.a.j 1
1848.2.a.k 1
1848.2.a.l 1
1848.2.a.m 2
1848.2.a.n 2
1848.2.a.o 2
1848.2.a.p 2
1848.2.a.q 2
1848.2.a.r 2
1848.2.a.s 2
1848.2.a.t 3
1848.2.a.u 3
1848.2.d $$\chi_{1848}(727, \cdot)$$ None 0 1
1848.2.e $$\chi_{1848}(923, \cdot)$$ n/a 376 1
1848.2.f $$\chi_{1848}(1121, \cdot)$$ 1848.2.f.a 36 1
1848.2.f.b 36
1848.2.g $$\chi_{1848}(925, \cdot)$$ n/a 120 1
1848.2.j $$\chi_{1848}(43, \cdot)$$ n/a 144 1
1848.2.k $$\chi_{1848}(1079, \cdot)$$ None 0 1
1848.2.p $$\chi_{1848}(1805, \cdot)$$ n/a 320 1
1848.2.q $$\chi_{1848}(769, \cdot)$$ 1848.2.q.a 24 1
1848.2.q.b 24
1848.2.t $$\chi_{1848}(967, \cdot)$$ None 0 1
1848.2.u $$\chi_{1848}(155, \cdot)$$ n/a 240 1
1848.2.v $$\chi_{1848}(881, \cdot)$$ 1848.2.v.a 8 1
1848.2.v.b 8
1848.2.v.c 16
1848.2.v.d 16
1848.2.v.e 32
1848.2.w $$\chi_{1848}(1693, \cdot)$$ n/a 192 1
1848.2.z $$\chi_{1848}(1651, \cdot)$$ n/a 160 1
1848.2.ba $$\chi_{1848}(1847, \cdot)$$ None 0 1
1848.2.bf $$\chi_{1848}(197, \cdot)$$ n/a 288 1
1848.2.bg $$\chi_{1848}(529, \cdot)$$ 1848.2.bg.a 2 2
1848.2.bg.b 2
1848.2.bg.c 4
1848.2.bg.d 6
1848.2.bg.e 6
1848.2.bg.f 8
1848.2.bg.g 8
1848.2.bg.h 10
1848.2.bg.i 10
1848.2.bg.j 12
1848.2.bg.k 12
1848.2.bh $$\chi_{1848}(169, \cdot)$$ n/a 144 4
1848.2.bk $$\chi_{1848}(901, \cdot)$$ n/a 384 2
1848.2.bl $$\chi_{1848}(89, \cdot)$$ n/a 160 2
1848.2.bm $$\chi_{1848}(683, \cdot)$$ n/a 640 2
1848.2.bn $$\chi_{1848}(1495, \cdot)$$ None 0 2
1848.2.bq $$\chi_{1848}(725, \cdot)$$ n/a 752 2
1848.2.bv $$\chi_{1848}(1055, \cdot)$$ None 0 2
1848.2.bw $$\chi_{1848}(859, \cdot)$$ n/a 320 2
1848.2.bz $$\chi_{1848}(1453, \cdot)$$ n/a 320 2
1848.2.ca $$\chi_{1848}(65, \cdot)$$ n/a 192 2
1848.2.cb $$\chi_{1848}(131, \cdot)$$ n/a 752 2
1848.2.cc $$\chi_{1848}(199, \cdot)$$ None 0 2
1848.2.cf $$\chi_{1848}(241, \cdot)$$ 1848.2.cf.a 48 2
1848.2.cf.b 48
1848.2.cg $$\chi_{1848}(1013, \cdot)$$ n/a 640 2
1848.2.cl $$\chi_{1848}(23, \cdot)$$ None 0 2
1848.2.cm $$\chi_{1848}(571, \cdot)$$ n/a 384 2
1848.2.cn $$\chi_{1848}(29, \cdot)$$ n/a 1152 4
1848.2.cs $$\chi_{1848}(643, \cdot)$$ n/a 768 4
1848.2.ct $$\chi_{1848}(167, \cdot)$$ None 0 4
1848.2.cw $$\chi_{1848}(377, \cdot)$$ n/a 384 4
1848.2.cx $$\chi_{1848}(13, \cdot)$$ n/a 768 4
1848.2.cy $$\chi_{1848}(127, \cdot)$$ None 0 4
1848.2.cz $$\chi_{1848}(323, \cdot)$$ n/a 1152 4
1848.2.dc $$\chi_{1848}(125, \cdot)$$ n/a 1504 4
1848.2.dd $$\chi_{1848}(601, \cdot)$$ n/a 192 4
1848.2.di $$\chi_{1848}(211, \cdot)$$ n/a 576 4
1848.2.dj $$\chi_{1848}(71, \cdot)$$ None 0 4
1848.2.dm $$\chi_{1848}(281, \cdot)$$ n/a 288 4
1848.2.dn $$\chi_{1848}(421, \cdot)$$ n/a 576 4
1848.2.do $$\chi_{1848}(223, \cdot)$$ None 0 4
1848.2.dp $$\chi_{1848}(83, \cdot)$$ n/a 1504 4
1848.2.ds $$\chi_{1848}(25, \cdot)$$ n/a 384 8
1848.2.dt $$\chi_{1848}(191, \cdot)$$ None 0 8
1848.2.du $$\chi_{1848}(403, \cdot)$$ n/a 1536 8
1848.2.dz $$\chi_{1848}(73, \cdot)$$ n/a 384 8
1848.2.ea $$\chi_{1848}(5, \cdot)$$ n/a 3008 8
1848.2.ed $$\chi_{1848}(227, \cdot)$$ n/a 3008 8
1848.2.ee $$\chi_{1848}(31, \cdot)$$ None 0 8
1848.2.ef $$\chi_{1848}(37, \cdot)$$ n/a 1536 8
1848.2.eg $$\chi_{1848}(233, \cdot)$$ n/a 768 8
1848.2.ej $$\chi_{1848}(215, \cdot)$$ None 0 8
1848.2.ek $$\chi_{1848}(115, \cdot)$$ n/a 1536 8
1848.2.ep $$\chi_{1848}(149, \cdot)$$ n/a 3008 8
1848.2.es $$\chi_{1848}(179, \cdot)$$ n/a 3008 8
1848.2.et $$\chi_{1848}(79, \cdot)$$ None 0 8
1848.2.eu $$\chi_{1848}(61, \cdot)$$ n/a 1536 8
1848.2.ev $$\chi_{1848}(185, \cdot)$$ n/a 768 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1848))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1848)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(462))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(616))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(924))$$$$^{\oplus 2}$$