# Properties

 Label 1904.2 Level 1904 Weight 2 Dimension 58526 Nonzero newspaces 52 Sturm bound 442368 Trace bound 61

## Defining parameters

 Level: $$N$$ = $$1904 = 2^{4} \cdot 7 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$52$$ Sturm bound: $$442368$$ Trace bound: $$61$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1904))$$.

Total New Old
Modular forms 113280 59878 53402
Cusp forms 107905 58526 49379
Eisenstein series 5375 1352 4023

## Trace form

 $$58526 q - 112 q^{2} - 86 q^{3} - 104 q^{4} - 138 q^{5} - 88 q^{6} - 102 q^{7} - 256 q^{8} - 26 q^{9} + O(q^{10})$$ $$58526 q - 112 q^{2} - 86 q^{3} - 104 q^{4} - 138 q^{5} - 88 q^{6} - 102 q^{7} - 256 q^{8} - 26 q^{9} - 104 q^{10} - 70 q^{11} - 120 q^{12} - 132 q^{13} - 144 q^{14} - 188 q^{15} - 136 q^{16} - 269 q^{17} - 224 q^{18} - 42 q^{19} - 88 q^{20} - 138 q^{21} - 272 q^{22} - 42 q^{23} - 104 q^{24} + 22 q^{25} - 88 q^{26} - 68 q^{27} - 120 q^{28} - 292 q^{29} - 120 q^{30} - 94 q^{31} - 72 q^{32} - 186 q^{33} - 108 q^{34} - 194 q^{35} - 288 q^{36} - 82 q^{37} - 152 q^{38} - 84 q^{39} - 136 q^{40} - 20 q^{41} - 280 q^{42} - 176 q^{43} - 216 q^{44} - 200 q^{45} - 176 q^{46} - 50 q^{47} - 312 q^{48} - 362 q^{49} - 464 q^{50} - 109 q^{51} - 464 q^{52} - 234 q^{53} - 440 q^{54} - 60 q^{55} - 320 q^{56} - 132 q^{57} - 320 q^{58} - 54 q^{59} - 440 q^{60} - 170 q^{61} - 256 q^{62} - 10 q^{63} - 440 q^{64} - 156 q^{65} - 328 q^{66} - 62 q^{67} - 176 q^{68} - 124 q^{69} - 216 q^{70} - 48 q^{71} - 280 q^{72} + 150 q^{73} - 104 q^{74} + 312 q^{75} - 56 q^{76} - 2 q^{77} - 288 q^{78} + 102 q^{79} - 72 q^{80} + 48 q^{81} - 104 q^{82} + 112 q^{83} - 152 q^{84} - 282 q^{85} - 232 q^{86} + 12 q^{87} - 72 q^{88} + 70 q^{89} + 24 q^{90} - 220 q^{91} - 344 q^{92} + 6 q^{93} - 24 q^{94} - 198 q^{95} + 72 q^{96} - 196 q^{97} - 8 q^{98} - 488 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1904))$$

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
1904.2.a $$\chi_{1904}(1, \cdot)$$ 1904.2.a.a 1 1
1904.2.a.b 1
1904.2.a.c 1
1904.2.a.d 1
1904.2.a.e 1
1904.2.a.f 2
1904.2.a.g 2
1904.2.a.h 2
1904.2.a.i 2
1904.2.a.j 2
1904.2.a.k 2
1904.2.a.l 2
1904.2.a.m 3
1904.2.a.n 3
1904.2.a.o 3
1904.2.a.p 3
1904.2.a.q 4
1904.2.a.r 4
1904.2.a.s 4
1904.2.a.t 5
1904.2.b $$\chi_{1904}(953, \cdot)$$ None 0 1
1904.2.c $$\chi_{1904}(1121, \cdot)$$ 1904.2.c.a 2 1
1904.2.c.b 2
1904.2.c.c 4
1904.2.c.d 4
1904.2.c.e 6
1904.2.c.f 8
1904.2.c.g 8
1904.2.c.h 10
1904.2.c.i 10
1904.2.h $$\chi_{1904}(1903, \cdot)$$ 1904.2.h.a 8 1
1904.2.h.b 16
1904.2.h.c 48
1904.2.i $$\chi_{1904}(1735, \cdot)$$ None 0 1
1904.2.j $$\chi_{1904}(783, \cdot)$$ 1904.2.j.a 8 1
1904.2.j.b 24
1904.2.j.c 32
1904.2.k $$\chi_{1904}(951, \cdot)$$ None 0 1
1904.2.p $$\chi_{1904}(169, \cdot)$$ None 0 1
1904.2.q $$\chi_{1904}(1089, \cdot)$$ n/a 128 2
1904.2.s $$\chi_{1904}(1203, \cdot)$$ n/a 568 2
1904.2.t $$\chi_{1904}(1373, \cdot)$$ n/a 432 2
1904.2.w $$\chi_{1904}(1177, \cdot)$$ None 0 2
1904.2.x $$\chi_{1904}(1007, \cdot)$$ n/a 144 2
1904.2.z $$\chi_{1904}(475, \cdot)$$ n/a 568 2
1904.2.bc $$\chi_{1904}(307, \cdot)$$ n/a 512 2
1904.2.be $$\chi_{1904}(477, \cdot)$$ n/a 384 2
1904.2.bf $$\chi_{1904}(645, \cdot)$$ n/a 432 2
1904.2.bi $$\chi_{1904}(225, \cdot)$$ n/a 108 2
1904.2.bj $$\chi_{1904}(55, \cdot)$$ None 0 2
1904.2.bm $$\chi_{1904}(421, \cdot)$$ n/a 432 2
1904.2.bn $$\chi_{1904}(251, \cdot)$$ n/a 568 2
1904.2.bp $$\chi_{1904}(1257, \cdot)$$ None 0 2
1904.2.bu $$\chi_{1904}(1055, \cdot)$$ n/a 128 2
1904.2.bv $$\chi_{1904}(1223, \cdot)$$ None 0 2
1904.2.bw $$\chi_{1904}(271, \cdot)$$ n/a 144 2
1904.2.bx $$\chi_{1904}(103, \cdot)$$ None 0 2
1904.2.cc $$\chi_{1904}(137, \cdot)$$ None 0 2
1904.2.cd $$\chi_{1904}(305, \cdot)$$ n/a 140 2
1904.2.ce $$\chi_{1904}(1063, \cdot)$$ None 0 4
1904.2.cg $$\chi_{1904}(1233, \cdot)$$ n/a 216 4
1904.2.ci $$\chi_{1904}(83, \cdot)$$ n/a 1136 4
1904.2.ck $$\chi_{1904}(253, \cdot)$$ n/a 864 4
1904.2.cm $$\chi_{1904}(195, \cdot)$$ n/a 1136 4
1904.2.co $$\chi_{1904}(365, \cdot)$$ n/a 864 4
1904.2.cq $$\chi_{1904}(111, \cdot)$$ n/a 288 4
1904.2.cs $$\chi_{1904}(281, \cdot)$$ None 0 4
1904.2.cv $$\chi_{1904}(523, \cdot)$$ n/a 1136 4
1904.2.cw $$\chi_{1904}(149, \cdot)$$ n/a 1136 4
1904.2.cy $$\chi_{1904}(361, \cdot)$$ None 0 4
1904.2.db $$\chi_{1904}(47, \cdot)$$ n/a 288 4
1904.2.dc $$\chi_{1904}(171, \cdot)$$ n/a 1024 4
1904.2.df $$\chi_{1904}(339, \cdot)$$ n/a 1136 4
1904.2.dh $$\chi_{1904}(373, \cdot)$$ n/a 1136 4
1904.2.di $$\chi_{1904}(205, \cdot)$$ n/a 1024 4
1904.2.dk $$\chi_{1904}(81, \cdot)$$ n/a 280 4
1904.2.dn $$\chi_{1904}(327, \cdot)$$ None 0 4
1904.2.dp $$\chi_{1904}(557, \cdot)$$ n/a 1136 4
1904.2.dq $$\chi_{1904}(115, \cdot)$$ n/a 1136 4
1904.2.dt $$\chi_{1904}(99, \cdot)$$ n/a 1728 8
1904.2.dv $$\chi_{1904}(125, \cdot)$$ n/a 2272 8
1904.2.dw $$\chi_{1904}(71, \cdot)$$ None 0 8
1904.2.dz $$\chi_{1904}(351, \cdot)$$ n/a 432 8
1904.2.ea $$\chi_{1904}(97, \cdot)$$ n/a 560 8
1904.2.ed $$\chi_{1904}(41, \cdot)$$ None 0 8
1904.2.ef $$\chi_{1904}(211, \cdot)$$ n/a 1728 8
1904.2.eh $$\chi_{1904}(181, \cdot)$$ n/a 2272 8
1904.2.ej $$\chi_{1904}(417, \cdot)$$ n/a 560 8
1904.2.el $$\chi_{1904}(87, \cdot)$$ None 0 8
1904.2.en $$\chi_{1904}(53, \cdot)$$ n/a 2272 8
1904.2.ep $$\chi_{1904}(451, \cdot)$$ n/a 2272 8
1904.2.er $$\chi_{1904}(485, \cdot)$$ n/a 2272 8
1904.2.et $$\chi_{1904}(19, \cdot)$$ n/a 2272 8
1904.2.ev $$\chi_{1904}(9, \cdot)$$ None 0 8
1904.2.ex $$\chi_{1904}(383, \cdot)$$ n/a 576 8
1904.2.ey $$\chi_{1904}(5, \cdot)$$ n/a 4544 16
1904.2.fa $$\chi_{1904}(11, \cdot)$$ n/a 4544 16
1904.2.fd $$\chi_{1904}(73, \cdot)$$ None 0 16
1904.2.fe $$\chi_{1904}(129, \cdot)$$ n/a 1120 16
1904.2.fh $$\chi_{1904}(79, \cdot)$$ n/a 1152 16
1904.2.fi $$\chi_{1904}(23, \cdot)$$ None 0 16
1904.2.fk $$\chi_{1904}(173, \cdot)$$ n/a 4544 16
1904.2.fm $$\chi_{1904}(107, \cdot)$$ n/a 4544 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1904))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1904)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(136))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(272))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(476))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(952))$$$$^{\oplus 2}$$