# Properties

 Label 847.2 Level 847 Weight 2 Dimension 26671 Nonzero newspaces 16 Newform subspaces 106 Sturm bound 116160 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$847 = 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$106$$ Sturm bound: $$116160$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(847))$$.

Total New Old
Modular forms 30000 28075 1925
Cusp forms 28081 26671 1410
Eisenstein series 1919 1404 515

## Trace form

 $$26671q - 177q^{2} - 176q^{3} - 173q^{4} - 174q^{5} - 188q^{6} - 234q^{7} - 475q^{8} - 207q^{9} + O(q^{10})$$ $$26671q - 177q^{2} - 176q^{3} - 173q^{4} - 174q^{5} - 188q^{6} - 234q^{7} - 475q^{8} - 207q^{9} - 222q^{10} - 210q^{11} - 392q^{12} - 186q^{13} - 252q^{14} - 506q^{15} - 269q^{16} - 222q^{17} - 261q^{18} - 220q^{19} - 278q^{20} - 271q^{21} - 560q^{22} - 376q^{23} - 340q^{24} - 269q^{25} - 318q^{26} - 260q^{27} - 328q^{28} - 520q^{29} - 368q^{30} - 228q^{31} - 317q^{32} - 280q^{33} - 446q^{34} - 309q^{35} - 719q^{36} - 262q^{37} - 340q^{38} - 344q^{39} - 430q^{40} - 318q^{41} - 403q^{42} - 586q^{43} - 340q^{44} - 542q^{45} - 368q^{46} - 272q^{47} - 516q^{48} - 334q^{49} - 677q^{50} - 368q^{51} - 422q^{52} - 346q^{53} - 560q^{54} - 320q^{55} - 630q^{56} - 670q^{57} - 430q^{58} - 320q^{59} - 312q^{60} - 238q^{61} - 384q^{62} - 222q^{63} - 603q^{64} - 216q^{65} - 210q^{66} - 412q^{67} - 194q^{68} - 144q^{69} - 117q^{70} - 418q^{71} - 25q^{72} - 186q^{73} - 286q^{74} - 36q^{75} + 80q^{76} - 245q^{77} - 802q^{78} - 260q^{79} - 134q^{80} - 39q^{81} - 234q^{82} - 256q^{83} + 93q^{84} - 522q^{85} - 148q^{86} - 220q^{87} - 340q^{88} - 390q^{89} - 366q^{90} - 261q^{91} - 702q^{92} - 392q^{93} - 536q^{94} - 460q^{95} - 468q^{96} - 482q^{97} - 472q^{98} - 780q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(847))$$

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
847.2.a $$\chi_{847}(1, \cdot)$$ 847.2.a.a 1 1
847.2.a.b 1
847.2.a.c 1
847.2.a.d 2
847.2.a.e 2
847.2.a.f 2
847.2.a.g 2
847.2.a.h 2
847.2.a.i 3
847.2.a.j 3
847.2.a.k 4
847.2.a.l 4
847.2.a.m 6
847.2.a.n 6
847.2.a.o 8
847.2.a.p 8
847.2.b $$\chi_{847}(846, \cdot)$$ 847.2.b.a 8 1
847.2.b.b 8
847.2.b.c 8
847.2.b.d 8
847.2.b.e 16
847.2.b.f 16
847.2.e $$\chi_{847}(485, \cdot)$$ 847.2.e.a 4 2
847.2.e.b 4
847.2.e.c 6
847.2.e.d 6
847.2.e.e 12
847.2.e.f 14
847.2.e.g 14
847.2.e.h 20
847.2.e.i 20
847.2.e.j 28
847.2.f $$\chi_{847}(148, \cdot)$$ 847.2.f.a 4 4
847.2.f.b 4
847.2.f.c 4
847.2.f.d 4
847.2.f.e 4
847.2.f.f 4
847.2.f.g 4
847.2.f.h 4
847.2.f.i 4
847.2.f.j 4
847.2.f.k 4
847.2.f.l 4
847.2.f.m 4
847.2.f.n 4
847.2.f.o 8
847.2.f.p 8
847.2.f.q 8
847.2.f.r 8
847.2.f.s 8
847.2.f.t 12
847.2.f.u 12
847.2.f.v 16
847.2.f.w 16
847.2.f.x 16
847.2.f.y 24
847.2.f.z 24
847.2.i $$\chi_{847}(241, \cdot)$$ 847.2.i.a 24 2
847.2.i.b 48
847.2.i.c 56
847.2.l $$\chi_{847}(118, \cdot)$$ 847.2.l.a 8 4
847.2.l.b 8
847.2.l.c 8
847.2.l.d 8
847.2.l.e 16
847.2.l.f 16
847.2.l.g 16
847.2.l.h 16
847.2.l.i 16
847.2.l.j 16
847.2.l.k 32
847.2.l.l 32
847.2.l.m 64
847.2.m $$\chi_{847}(78, \cdot)$$ 847.2.m.a 320 10
847.2.m.b 340
847.2.n $$\chi_{847}(9, \cdot)$$ 847.2.n.a 8 8
847.2.n.b 8
847.2.n.c 8
847.2.n.d 24
847.2.n.e 24
847.2.n.f 24
847.2.n.g 24
847.2.n.h 40
847.2.n.i 40
847.2.n.j 40
847.2.n.k 48
847.2.n.l 56
847.2.n.m 56
847.2.n.n 112
847.2.p $$\chi_{847}(76, \cdot)$$ 847.2.p.a 20 10
847.2.p.b 840
847.2.r $$\chi_{847}(40, \cdot)$$ 847.2.r.a 48 8
847.2.r.b 48
847.2.r.c 48
847.2.r.d 48
847.2.r.e 96
847.2.r.f 224
847.2.u $$\chi_{847}(23, \cdot)$$ 847.2.u.a 1720 20
847.2.v $$\chi_{847}(15, \cdot)$$ 847.2.v.a 1280 40
847.2.v.b 1360
847.2.x $$\chi_{847}(10, \cdot)$$ 847.2.x.a 1720 20
847.2.ba $$\chi_{847}(6, \cdot)$$ 847.2.ba.a 80 40
847.2.ba.b 3360
847.2.bc $$\chi_{847}(4, \cdot)$$ 847.2.bc.a 6880 80
847.2.be $$\chi_{847}(17, \cdot)$$ 847.2.be.a 6880 80

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(847))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(847)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 2}$$