# Properties

 Label 1856.2 Level 1856 Weight 2 Dimension 59742 Nonzero newspaces 28 Sturm bound 430080 Trace bound 15

## Defining parameters

 Level: $$N$$ = $$1856 = 2^{6} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Sturm bound: $$430080$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1856))$$.

Total New Old
Modular forms 109536 60930 48606
Cusp forms 105505 59742 45763
Eisenstein series 4031 1188 2843

## Trace form

 $$59742 q - 208 q^{2} - 156 q^{3} - 208 q^{4} - 208 q^{5} - 208 q^{6} - 152 q^{7} - 208 q^{8} - 254 q^{9} + O(q^{10})$$ $$59742 q - 208 q^{2} - 156 q^{3} - 208 q^{4} - 208 q^{5} - 208 q^{6} - 152 q^{7} - 208 q^{8} - 254 q^{9} - 208 q^{10} - 148 q^{11} - 208 q^{12} - 192 q^{13} - 208 q^{14} - 144 q^{15} - 208 q^{16} - 348 q^{17} - 208 q^{18} - 140 q^{19} - 208 q^{20} - 216 q^{21} - 224 q^{22} - 152 q^{23} - 288 q^{24} - 282 q^{25} - 288 q^{26} - 168 q^{27} - 288 q^{28} - 232 q^{29} - 592 q^{30} - 200 q^{31} - 288 q^{32} - 208 q^{33} - 288 q^{34} - 160 q^{35} - 368 q^{36} - 224 q^{37} - 288 q^{38} - 152 q^{39} - 288 q^{40} - 260 q^{41} - 288 q^{42} - 132 q^{43} - 224 q^{44} - 200 q^{45} - 208 q^{46} - 120 q^{47} - 208 q^{48} - 346 q^{49} - 160 q^{50} - 208 q^{51} - 112 q^{52} - 160 q^{53} - 80 q^{54} - 280 q^{55} - 96 q^{56} - 248 q^{57} - 144 q^{58} - 460 q^{59} - 16 q^{60} - 192 q^{61} - 144 q^{62} - 288 q^{63} - 16 q^{64} - 568 q^{65} - 48 q^{66} - 332 q^{67} - 112 q^{68} - 184 q^{69} - 16 q^{70} - 280 q^{71} - 64 q^{72} - 260 q^{73} - 96 q^{74} - 268 q^{75} - 80 q^{76} - 216 q^{77} - 160 q^{78} - 216 q^{79} - 288 q^{80} - 370 q^{81} - 368 q^{82} - 156 q^{83} - 432 q^{84} - 224 q^{85} - 416 q^{86} - 160 q^{87} - 592 q^{88} - 356 q^{89} - 496 q^{90} - 144 q^{91} - 512 q^{92} - 288 q^{93} - 400 q^{94} - 192 q^{95} - 480 q^{96} - 236 q^{97} - 480 q^{98} - 204 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1856))$$

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
1856.2.a $$\chi_{1856}(1, \cdot)$$ 1856.2.a.a 1 1
1856.2.a.b 1
1856.2.a.c 1
1856.2.a.d 1
1856.2.a.e 1
1856.2.a.f 1
1856.2.a.g 1
1856.2.a.h 1
1856.2.a.i 1
1856.2.a.j 1
1856.2.a.k 1
1856.2.a.l 1
1856.2.a.m 1
1856.2.a.n 1
1856.2.a.o 1
1856.2.a.p 1
1856.2.a.q 2
1856.2.a.r 2
1856.2.a.s 2
1856.2.a.t 2
1856.2.a.u 2
1856.2.a.v 2
1856.2.a.w 2
1856.2.a.x 3
1856.2.a.y 3
1856.2.a.z 4
1856.2.a.ba 5
1856.2.a.bb 5
1856.2.a.bc 6
1856.2.c $$\chi_{1856}(929, \cdot)$$ 1856.2.c.a 8 1
1856.2.c.b 8
1856.2.c.c 20
1856.2.c.d 20
1856.2.e $$\chi_{1856}(1217, \cdot)$$ 1856.2.e.a 2 1
1856.2.e.b 2
1856.2.e.c 2
1856.2.e.d 2
1856.2.e.e 2
1856.2.e.f 2
1856.2.e.g 2
1856.2.e.h 4
1856.2.e.i 8
1856.2.e.j 8
1856.2.e.k 12
1856.2.e.l 12
1856.2.g $$\chi_{1856}(289, \cdot)$$ 1856.2.g.a 4 1
1856.2.g.b 16
1856.2.g.c 40
1856.2.j $$\chi_{1856}(911, \cdot)$$ n/a 116 2
1856.2.k $$\chi_{1856}(191, \cdot)$$ n/a 116 2
1856.2.m $$\chi_{1856}(753, \cdot)$$ n/a 116 2
1856.2.n $$\chi_{1856}(465, \cdot)$$ n/a 112 2
1856.2.q $$\chi_{1856}(1119, \cdot)$$ n/a 120 2
1856.2.t $$\chi_{1856}(655, \cdot)$$ n/a 116 2
1856.2.u $$\chi_{1856}(65, \cdot)$$ n/a 348 6
1856.2.v $$\chi_{1856}(233, \cdot)$$ None 0 4
1856.2.x $$\chi_{1856}(679, \cdot)$$ None 0 4
1856.2.ba $$\chi_{1856}(215, \cdot)$$ None 0 4
1856.2.bc $$\chi_{1856}(57, \cdot)$$ None 0 4
1856.2.be $$\chi_{1856}(33, \cdot)$$ n/a 360 6
1856.2.bg $$\chi_{1856}(129, \cdot)$$ n/a 348 6
1856.2.bi $$\chi_{1856}(161, \cdot)$$ n/a 360 6
1856.2.bl $$\chi_{1856}(307, \cdot)$$ n/a 1904 8
1856.2.bn $$\chi_{1856}(117, \cdot)$$ n/a 1792 8
1856.2.bp $$\chi_{1856}(173, \cdot)$$ n/a 1904 8
1856.2.bq $$\chi_{1856}(75, \cdot)$$ n/a 1904 8
1856.2.bs $$\chi_{1856}(47, \cdot)$$ n/a 696 12
1856.2.bv $$\chi_{1856}(31, \cdot)$$ n/a 720 12
1856.2.by $$\chi_{1856}(49, \cdot)$$ n/a 696 12
1856.2.bz $$\chi_{1856}(209, \cdot)$$ n/a 696 12
1856.2.cb $$\chi_{1856}(127, \cdot)$$ n/a 696 12
1856.2.cc $$\chi_{1856}(15, \cdot)$$ n/a 696 12
1856.2.cf $$\chi_{1856}(9, \cdot)$$ None 0 24
1856.2.ch $$\chi_{1856}(55, \cdot)$$ None 0 24
1856.2.ci $$\chi_{1856}(39, \cdot)$$ None 0 24
1856.2.ck $$\chi_{1856}(25, \cdot)$$ None 0 24
1856.2.cm $$\chi_{1856}(11, \cdot)$$ n/a 11424 48
1856.2.co $$\chi_{1856}(5, \cdot)$$ n/a 11424 48
1856.2.cq $$\chi_{1856}(45, \cdot)$$ n/a 11424 48
1856.2.ct $$\chi_{1856}(3, \cdot)$$ n/a 11424 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1856))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1856)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(232))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(928))$$$$^{\oplus 2}$$