# Properties

 Label 1824.2 Level 1824 Weight 2 Dimension 38324 Nonzero newspaces 36 Sturm bound 368640 Trace bound 49

## Defining parameters

 Level: $$N$$ = $$1824 = 2^{5} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$368640$$ Trace bound: $$49$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1824))$$.

Total New Old
Modular forms 94464 39004 55460
Cusp forms 89857 38324 51533
Eisenstein series 4607 680 3927

## Trace form

 $$38324 q - 50 q^{3} - 128 q^{4} - 8 q^{5} - 64 q^{6} - 100 q^{7} - 104 q^{9} + O(q^{10})$$ $$38324 q - 50 q^{3} - 128 q^{4} - 8 q^{5} - 64 q^{6} - 100 q^{7} - 104 q^{9} - 96 q^{10} - 32 q^{12} - 104 q^{13} + 64 q^{14} - 30 q^{15} - 48 q^{16} + 32 q^{17} - 48 q^{18} - 96 q^{19} + 64 q^{20} - 32 q^{21} - 80 q^{22} + 48 q^{23} - 88 q^{24} - 156 q^{25} - 80 q^{26} + 22 q^{27} - 208 q^{28} - 8 q^{29} - 160 q^{30} - 4 q^{31} - 80 q^{32} - 164 q^{33} - 176 q^{34} + 96 q^{35} - 168 q^{36} - 168 q^{37} - 40 q^{38} - 68 q^{39} - 208 q^{40} - 16 q^{41} - 184 q^{42} - 100 q^{43} - 16 q^{44} - 136 q^{45} - 128 q^{46} - 48 q^{47} - 168 q^{48} - 148 q^{49} - 48 q^{50} - 86 q^{51} - 224 q^{52} + 24 q^{53} - 168 q^{54} - 220 q^{55} - 112 q^{56} - 124 q^{57} - 416 q^{58} - 128 q^{59} - 184 q^{60} - 8 q^{61} - 96 q^{62} - 78 q^{63} - 272 q^{64} - 16 q^{65} - 112 q^{66} - 196 q^{67} + 16 q^{68} + 64 q^{69} - 176 q^{70} - 80 q^{71} + 56 q^{72} - 112 q^{73} + 64 q^{74} - 112 q^{75} - 136 q^{76} + 128 q^{77} + 64 q^{78} - 100 q^{79} + 112 q^{80} + 40 q^{81} + 32 q^{82} + 200 q^{84} + 128 q^{86} - 182 q^{87} + 48 q^{88} + 200 q^{90} - 92 q^{91} + 160 q^{92} - 88 q^{93} + 48 q^{94} - 16 q^{95} + 144 q^{96} - 304 q^{97} + 160 q^{98} - 206 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1824))$$

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
1824.2.a $$\chi_{1824}(1, \cdot)$$ 1824.2.a.a 1 1
1824.2.a.b 1
1824.2.a.c 1
1824.2.a.d 1
1824.2.a.e 1
1824.2.a.f 1
1824.2.a.g 1
1824.2.a.h 1
1824.2.a.i 1
1824.2.a.j 1
1824.2.a.k 1
1824.2.a.l 1
1824.2.a.m 2
1824.2.a.n 2
1824.2.a.o 2
1824.2.a.p 2
1824.2.a.q 2
1824.2.a.r 2
1824.2.a.s 3
1824.2.a.t 3
1824.2.a.u 3
1824.2.a.v 3
1824.2.d $$\chi_{1824}(191, \cdot)$$ 1824.2.d.a 4 1
1824.2.d.b 4
1824.2.d.c 4
1824.2.d.d 4
1824.2.d.e 4
1824.2.d.f 20
1824.2.d.g 32
1824.2.e $$\chi_{1824}(1519, \cdot)$$ 1824.2.e.a 40 1
1824.2.f $$\chi_{1824}(1025, \cdot)$$ 1824.2.f.a 4 1
1824.2.f.b 4
1824.2.f.c 4
1824.2.f.d 4
1824.2.f.e 16
1824.2.f.f 16
1824.2.f.g 16
1824.2.f.h 16
1824.2.g $$\chi_{1824}(913, \cdot)$$ 1824.2.g.a 18 1
1824.2.g.b 18
1824.2.j $$\chi_{1824}(1103, \cdot)$$ 1824.2.j.a 4 1
1824.2.j.b 8
1824.2.j.c 12
1824.2.j.d 24
1824.2.j.e 24
1824.2.k $$\chi_{1824}(607, \cdot)$$ 1824.2.k.a 20 1
1824.2.k.b 20
1824.2.p $$\chi_{1824}(113, \cdot)$$ 1824.2.p.a 12 1
1824.2.p.b 64
1824.2.q $$\chi_{1824}(577, \cdot)$$ 1824.2.q.a 2 2
1824.2.q.b 2
1824.2.q.c 2
1824.2.q.d 2
1824.2.q.e 2
1824.2.q.f 2
1824.2.q.g 2
1824.2.q.h 2
1824.2.q.i 4
1824.2.q.j 4
1824.2.q.k 6
1824.2.q.l 6
1824.2.q.m 6
1824.2.q.n 6
1824.2.q.o 6
1824.2.q.p 6
1824.2.q.q 10
1824.2.q.r 10
1824.2.r $$\chi_{1824}(569, \cdot)$$ None 0 2
1824.2.u $$\chi_{1824}(457, \cdot)$$ None 0 2
1824.2.v $$\chi_{1824}(647, \cdot)$$ None 0 2
1824.2.y $$\chi_{1824}(151, \cdot)$$ None 0 2
1824.2.bb $$\chi_{1824}(31, \cdot)$$ 1824.2.bb.a 40 2
1824.2.bb.b 40
1824.2.bc $$\chi_{1824}(239, \cdot)$$ n/a 152 2
1824.2.bd $$\chi_{1824}(977, \cdot)$$ n/a 152 2
1824.2.bg $$\chi_{1824}(559, \cdot)$$ 1824.2.bg.a 80 2
1824.2.bh $$\chi_{1824}(767, \cdot)$$ n/a 160 2
1824.2.bm $$\chi_{1824}(49, \cdot)$$ 1824.2.bm.a 80 2
1824.2.bn $$\chi_{1824}(65, \cdot)$$ n/a 160 2
1824.2.bq $$\chi_{1824}(229, \cdot)$$ n/a 576 4
1824.2.br $$\chi_{1824}(379, \cdot)$$ n/a 640 4
1824.2.bs $$\chi_{1824}(419, \cdot)$$ n/a 1152 4
1824.2.bt $$\chi_{1824}(341, \cdot)$$ n/a 1264 4
1824.2.bw $$\chi_{1824}(289, \cdot)$$ n/a 240 6
1824.2.by $$\chi_{1824}(121, \cdot)$$ None 0 4
1824.2.bz $$\chi_{1824}(521, \cdot)$$ None 0 4
1824.2.cc $$\chi_{1824}(103, \cdot)$$ None 0 4
1824.2.cd $$\chi_{1824}(311, \cdot)$$ None 0 4
1824.2.ch $$\chi_{1824}(401, \cdot)$$ n/a 456 6
1824.2.ci $$\chi_{1824}(529, \cdot)$$ n/a 240 6
1824.2.ck $$\chi_{1824}(257, \cdot)$$ n/a 480 6
1824.2.cn $$\chi_{1824}(79, \cdot)$$ n/a 240 6
1824.2.cp $$\chi_{1824}(479, \cdot)$$ n/a 480 6
1824.2.cq $$\chi_{1824}(127, \cdot)$$ n/a 240 6
1824.2.cs $$\chi_{1824}(47, \cdot)$$ n/a 456 6
1824.2.cu $$\chi_{1824}(221, \cdot)$$ n/a 2528 8
1824.2.cv $$\chi_{1824}(11, \cdot)$$ n/a 2528 8
1824.2.da $$\chi_{1824}(259, \cdot)$$ n/a 1280 8
1824.2.db $$\chi_{1824}(277, \cdot)$$ n/a 1280 8
1824.2.dd $$\chi_{1824}(295, \cdot)$$ None 0 12
1824.2.df $$\chi_{1824}(23, \cdot)$$ None 0 12
1824.2.dg $$\chi_{1824}(25, \cdot)$$ None 0 12
1824.2.di $$\chi_{1824}(41, \cdot)$$ None 0 12
1824.2.dl $$\chi_{1824}(61, \cdot)$$ n/a 3840 24
1824.2.dm $$\chi_{1824}(67, \cdot)$$ n/a 3840 24
1824.2.do $$\chi_{1824}(29, \cdot)$$ n/a 7584 24
1824.2.dr $$\chi_{1824}(35, \cdot)$$ n/a 7584 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1824))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1824)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 2}$$