## Defining parameters

 Level: $$N$$ = $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Sturm bound: $$405504$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1840))$$.

Total New Old
Modular forms 103840 52642 51198
Cusp forms 98913 51506 47407
Eisenstein series 4927 1136 3791

## Trace form

 $$51506 q - 80 q^{2} - 62 q^{3} - 72 q^{4} - 149 q^{5} - 216 q^{6} - 54 q^{7} - 56 q^{8} - 14 q^{9} + O(q^{10})$$ $$51506 q - 80 q^{2} - 62 q^{3} - 72 q^{4} - 149 q^{5} - 216 q^{6} - 54 q^{7} - 56 q^{8} - 14 q^{9} - 116 q^{10} - 166 q^{11} - 88 q^{12} - 90 q^{13} - 88 q^{14} - 55 q^{15} - 264 q^{16} - 162 q^{17} - 64 q^{18} - 10 q^{19} - 108 q^{20} - 242 q^{21} - 72 q^{22} - 48 q^{23} - 160 q^{24} - 13 q^{25} - 216 q^{26} - 74 q^{27} - 104 q^{28} - 70 q^{29} - 188 q^{30} - 254 q^{31} - 120 q^{32} - 230 q^{33} - 184 q^{34} - 119 q^{35} - 376 q^{36} - 146 q^{37} - 232 q^{38} - 106 q^{39} - 292 q^{40} - 122 q^{41} - 232 q^{42} - 46 q^{43} - 200 q^{44} - 190 q^{45} - 288 q^{46} - 56 q^{47} - 168 q^{48} - 166 q^{49} - 228 q^{50} - 126 q^{51} - 152 q^{52} - 98 q^{53} - 168 q^{54} - 59 q^{55} - 264 q^{56} + 58 q^{57} - 120 q^{58} - 10 q^{59} - 52 q^{60} - 330 q^{61} - 8 q^{62} - 118 q^{63} - 24 q^{64} - 197 q^{65} - 88 q^{66} - 166 q^{67} + 40 q^{68} - 122 q^{69} - 88 q^{70} - 286 q^{71} + 184 q^{72} + 22 q^{73} + 104 q^{74} - 245 q^{75} - 56 q^{76} - 6 q^{77} + 184 q^{78} - 110 q^{79} + 60 q^{80} - 126 q^{81} + 56 q^{82} - 106 q^{83} + 200 q^{84} - 13 q^{85} - 104 q^{86} + 98 q^{87} + 136 q^{88} + 202 q^{89} + 116 q^{90} + 20 q^{91} - 88 q^{92} + 156 q^{93} - 24 q^{94} - 71 q^{95} - 168 q^{96} + 54 q^{97} - 160 q^{98} + 186 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1840))$$

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
1840.2.a $$\chi_{1840}(1, \cdot)$$ 1840.2.a.a 1 1
1840.2.a.b 1
1840.2.a.c 1
1840.2.a.d 1
1840.2.a.e 1
1840.2.a.f 1
1840.2.a.g 1
1840.2.a.h 1
1840.2.a.i 1
1840.2.a.j 2
1840.2.a.k 2
1840.2.a.l 2
1840.2.a.m 2
1840.2.a.n 2
1840.2.a.o 2
1840.2.a.p 2
1840.2.a.q 3
1840.2.a.r 3
1840.2.a.s 3
1840.2.a.t 3
1840.2.a.u 4
1840.2.a.v 5
1840.2.b $$\chi_{1840}(919, \cdot)$$ None 0 1
1840.2.e $$\chi_{1840}(369, \cdot)$$ 1840.2.e.a 2 1
1840.2.e.b 2
1840.2.e.c 4
1840.2.e.d 8
1840.2.e.e 8
1840.2.e.f 12
1840.2.e.g 14
1840.2.e.h 16
1840.2.f $$\chi_{1840}(921, \cdot)$$ None 0 1
1840.2.i $$\chi_{1840}(1471, \cdot)$$ 1840.2.i.a 16 1
1840.2.i.b 16
1840.2.i.c 16
1840.2.j $$\chi_{1840}(1289, \cdot)$$ None 0 1
1840.2.m $$\chi_{1840}(1839, \cdot)$$ 1840.2.m.a 4 1
1840.2.m.b 4
1840.2.m.c 4
1840.2.m.d 4
1840.2.m.e 8
1840.2.m.f 8
1840.2.m.g 40
1840.2.n $$\chi_{1840}(551, \cdot)$$ None 0 1
1840.2.r $$\chi_{1840}(413, \cdot)$$ n/a 568 2
1840.2.t $$\chi_{1840}(1243, \cdot)$$ n/a 528 2
1840.2.u $$\chi_{1840}(91, \cdot)$$ n/a 384 2
1840.2.x $$\chi_{1840}(461, \cdot)$$ n/a 352 2
1840.2.y $$\chi_{1840}(1057, \cdot)$$ n/a 140 2
1840.2.ba $$\chi_{1840}(47, \cdot)$$ n/a 132 2
1840.2.bd $$\chi_{1840}(967, \cdot)$$ None 0 2
1840.2.bf $$\chi_{1840}(137, \cdot)$$ None 0 2
1840.2.bg $$\chi_{1840}(829, \cdot)$$ n/a 528 2
1840.2.bj $$\chi_{1840}(459, \cdot)$$ n/a 568 2
1840.2.bk $$\chi_{1840}(323, \cdot)$$ n/a 528 2
1840.2.bm $$\chi_{1840}(1333, \cdot)$$ n/a 568 2
1840.2.bo $$\chi_{1840}(81, \cdot)$$ n/a 480 10
1840.2.br $$\chi_{1840}(471, \cdot)$$ None 0 10
1840.2.bs $$\chi_{1840}(79, \cdot)$$ n/a 720 10
1840.2.bv $$\chi_{1840}(9, \cdot)$$ None 0 10
1840.2.bw $$\chi_{1840}(111, \cdot)$$ n/a 480 10
1840.2.bz $$\chi_{1840}(41, \cdot)$$ None 0 10
1840.2.ca $$\chi_{1840}(49, \cdot)$$ n/a 700 10
1840.2.cd $$\chi_{1840}(199, \cdot)$$ None 0 10
1840.2.cf $$\chi_{1840}(53, \cdot)$$ n/a 5680 20
1840.2.ch $$\chi_{1840}(3, \cdot)$$ n/a 5680 20
1840.2.cj $$\chi_{1840}(19, \cdot)$$ n/a 5680 20
1840.2.ck $$\chi_{1840}(29, \cdot)$$ n/a 5680 20
1840.2.cm $$\chi_{1840}(57, \cdot)$$ None 0 20
1840.2.co $$\chi_{1840}(87, \cdot)$$ None 0 20
1840.2.cr $$\chi_{1840}(127, \cdot)$$ n/a 1440 20
1840.2.ct $$\chi_{1840}(17, \cdot)$$ n/a 1400 20
1840.2.cv $$\chi_{1840}(101, \cdot)$$ n/a 3840 20
1840.2.cw $$\chi_{1840}(11, \cdot)$$ n/a 3840 20
1840.2.cy $$\chi_{1840}(123, \cdot)$$ n/a 5680 20
1840.2.da $$\chi_{1840}(37, \cdot)$$ n/a 5680 20

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1840))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1840)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(368))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(920))$$$$^{\oplus 2}$$