# Properties

 Label 2842.2 Level 2842 Weight 2 Dimension 78805 Nonzero newspaces 54 Sturm bound 987840 Trace bound 21

## Defining parameters

 Level: $$N$$ = $$2842 = 2 \cdot 7^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$54$$ Sturm bound: $$987840$$ Trace bound: $$21$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2842))$$.

Total New Old
Modular forms 250320 78805 171515
Cusp forms 243601 78805 164796
Eisenstein series 6719 0 6719

## Trace form

 $$78805 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + O(q^{10})$$ $$78805 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + 12 q^{10} + 24 q^{11} + 12 q^{13} + 12 q^{14} + 48 q^{15} + 6 q^{16} + 60 q^{17} + 22 q^{18} + 48 q^{19} + 19 q^{20} + 52 q^{21} + 52 q^{22} + 76 q^{23} + 44 q^{24} + 98 q^{25} + 79 q^{26} + 180 q^{27} + 16 q^{28} + 74 q^{29} + 132 q^{30} + 104 q^{31} - 2 q^{32} + 180 q^{33} + 47 q^{34} + 84 q^{35} + 58 q^{36} - 24 q^{38} + 4 q^{39} - 65 q^{40} - 60 q^{41} - 108 q^{42} - 48 q^{43} - 60 q^{44} - 229 q^{45} - 204 q^{46} - 92 q^{47} - 28 q^{48} - 236 q^{49} - 86 q^{50} - 184 q^{51} - 16 q^{52} + 27 q^{53} - 188 q^{54} - 164 q^{55} - 72 q^{56} + 32 q^{57} - 42 q^{58} - 44 q^{59} - 36 q^{60} + 16 q^{61} - 4 q^{62} + 72 q^{63} + 6 q^{64} + 231 q^{65} + 96 q^{66} + 176 q^{67} + 60 q^{68} + 248 q^{69} + 84 q^{70} + 256 q^{71} + 22 q^{72} + 247 q^{73} + 152 q^{74} + 428 q^{75} + 104 q^{76} + 168 q^{77} + 192 q^{78} + 248 q^{79} + 12 q^{80} + 254 q^{81} + 116 q^{82} + 88 q^{83} + 52 q^{84} + 216 q^{85} + 196 q^{86} + 116 q^{87} + 24 q^{88} + 128 q^{89} + 296 q^{90} + 20 q^{91} + 132 q^{92} - 104 q^{93} + 200 q^{94} + 128 q^{95} + 16 q^{96} + 51 q^{97} + 96 q^{98} + 172 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2842))$$

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
2842.2.a $$\chi_{2842}(1, \cdot)$$ 2842.2.a.a 1 1
2842.2.a.b 1
2842.2.a.c 1
2842.2.a.d 1
2842.2.a.e 1
2842.2.a.f 1
2842.2.a.g 2
2842.2.a.h 2
2842.2.a.i 2
2842.2.a.j 2
2842.2.a.k 2
2842.2.a.l 2
2842.2.a.m 2
2842.2.a.n 3
2842.2.a.o 4
2842.2.a.p 4
2842.2.a.q 4
2842.2.a.r 4
2842.2.a.s 5
2842.2.a.t 5
2842.2.a.u 5
2842.2.a.v 5
2842.2.a.w 5
2842.2.a.x 5
2842.2.a.y 5
2842.2.a.z 5
2842.2.a.ba 6
2842.2.a.bb 6
2842.2.a.bc 6
2842.2.c $$\chi_{2842}(1275, \cdot)$$ n/a 102 1
2842.2.e $$\chi_{2842}(1451, \cdot)$$ n/a 184 2
2842.2.g $$\chi_{2842}(1665, \cdot)$$ n/a 200 2
2842.2.i $$\chi_{2842}(753, \cdot)$$ n/a 200 2
2842.2.k $$\chi_{2842}(1205, \cdot)$$ n/a 840 6
2842.2.l $$\chi_{2842}(575, \cdot)$$ n/a 840 6
2842.2.m $$\chi_{2842}(239, \cdot)$$ n/a 840 6
2842.2.n $$\chi_{2842}(407, \cdot)$$ n/a 768 6
2842.2.o $$\chi_{2842}(197, \cdot)$$ n/a 618 6
2842.2.p $$\chi_{2842}(1359, \cdot)$$ n/a 840 6
2842.2.q $$\chi_{2842}(1051, \cdot)$$ n/a 840 6
2842.2.r $$\chi_{2842}(141, \cdot)$$ n/a 840 6
2842.2.s $$\chi_{2842}(215, \cdot)$$ n/a 400 4
2842.2.u $$\chi_{2842}(477, \cdot)$$ n/a 840 6
2842.2.be $$\chi_{2842}(71, \cdot)$$ n/a 840 6
2842.2.bf $$\chi_{2842}(295, \cdot)$$ n/a 612 6
2842.2.bg $$\chi_{2842}(57, \cdot)$$ n/a 840 6
2842.2.bh $$\chi_{2842}(225, \cdot)$$ n/a 840 6
2842.2.bi $$\chi_{2842}(1695, \cdot)$$ n/a 840 6
2842.2.bj $$\chi_{2842}(183, \cdot)$$ n/a 840 6
2842.2.bq $$\chi_{2842}(323, \cdot)$$ n/a 840 6
2842.2.bs $$\chi_{2842}(53, \cdot)$$ n/a 1680 12
2842.2.bt $$\chi_{2842}(401, \cdot)$$ n/a 1680 12
2842.2.bu $$\chi_{2842}(165, \cdot)$$ n/a 1200 12
2842.2.bv $$\chi_{2842}(233, \cdot)$$ n/a 1584 12
2842.2.bw $$\chi_{2842}(23, \cdot)$$ n/a 1680 12
2842.2.bx $$\chi_{2842}(837, \cdot)$$ n/a 1680 12
2842.2.by $$\chi_{2842}(25, \cdot)$$ n/a 1680 12
2842.2.bz $$\chi_{2842}(123, \cdot)$$ n/a 1680 12
2842.2.cb $$\chi_{2842}(27, \cdot)$$ n/a 1680 12
2842.2.cc $$\chi_{2842}(461, \cdot)$$ n/a 1680 12
2842.2.cd $$\chi_{2842}(97, \cdot)$$ n/a 1200 12
2842.2.ce $$\chi_{2842}(41, \cdot)$$ n/a 1680 12
2842.2.cf $$\chi_{2842}(69, \cdot)$$ n/a 1680 12
2842.2.cg $$\chi_{2842}(503, \cdot)$$ n/a 1680 12
2842.2.ch $$\chi_{2842}(55, \cdot)$$ n/a 1680 12
2842.2.cp $$\chi_{2842}(153, \cdot)$$ n/a 1680 12
2842.2.cr $$\chi_{2842}(1173, \cdot)$$ n/a 1680 12
2842.2.cy $$\chi_{2842}(93, \cdot)$$ n/a 1680 12
2842.2.cz $$\chi_{2842}(151, \cdot)$$ n/a 1680 12
2842.2.da $$\chi_{2842}(51, \cdot)$$ n/a 1680 12
2842.2.db $$\chi_{2842}(499, \cdot)$$ n/a 1680 12
2842.2.dc $$\chi_{2842}(289, \cdot)$$ n/a 1680 12
2842.2.dd $$\chi_{2842}(67, \cdot)$$ n/a 1200 12
2842.2.dn $$\chi_{2842}(9, \cdot)$$ n/a 1680 12
2842.2.do $$\chi_{2842}(89, \cdot)$$ n/a 3360 24
2842.2.dw $$\chi_{2842}(229, \cdot)$$ n/a 3360 24
2842.2.dx $$\chi_{2842}(19, \cdot)$$ n/a 2400 24
2842.2.dy $$\chi_{2842}(101, \cdot)$$ n/a 3360 24
2842.2.dz $$\chi_{2842}(131, \cdot)$$ n/a 3360 24
2842.2.ea $$\chi_{2842}(17, \cdot)$$ n/a 3360 24
2842.2.eb $$\chi_{2842}(61, \cdot)$$ n/a 3360 24
2842.2.ec $$\chi_{2842}(3, \cdot)$$ n/a 3360 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2842))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2842)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(203))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(406))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1421))$$$$^{\oplus 2}$$