# Properties

 Label 1134.2 Level 1134 Weight 2 Dimension 8832 Nonzero newspaces 22 Sturm bound 139968 Trace bound 23

## Defining parameters

 Level: $$N$$ = $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$22$$ Sturm bound: $$139968$$ Trace bound: $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1134))$$.

Total New Old
Modular forms 36288 8832 27456
Cusp forms 33697 8832 24865
Eisenstein series 2591 0 2591

## Trace form

 $$8832 q - 12 q^{5} - 6 q^{7} - 6 q^{8} + O(q^{10})$$ $$8832 q - 12 q^{5} - 6 q^{7} - 6 q^{8} - 12 q^{10} - 30 q^{11} - 24 q^{13} - 6 q^{14} - 24 q^{17} + 18 q^{18} + 36 q^{19} + 60 q^{20} + 54 q^{21} + 42 q^{22} + 156 q^{23} + 72 q^{25} + 180 q^{26} + 108 q^{27} + 24 q^{28} + 168 q^{29} + 108 q^{30} + 72 q^{31} + 108 q^{33} + 30 q^{34} + 60 q^{35} + 36 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{40} + 6 q^{41} - 18 q^{43} - 12 q^{44} + 108 q^{45} - 24 q^{46} + 108 q^{47} + 48 q^{49} + 126 q^{51} + 12 q^{52} + 240 q^{53} + 216 q^{55} - 6 q^{56} + 108 q^{57} + 60 q^{58} + 318 q^{59} + 144 q^{61} + 96 q^{62} + 54 q^{63} - 6 q^{64} + 228 q^{65} - 144 q^{66} + 198 q^{67} + 48 q^{68} - 252 q^{69} + 132 q^{70} - 96 q^{71} - 144 q^{72} + 60 q^{73} - 120 q^{74} - 360 q^{75} + 66 q^{76} - 138 q^{77} - 288 q^{78} + 156 q^{79} - 48 q^{80} - 288 q^{81} - 12 q^{82} - 288 q^{83} - 36 q^{84} + 72 q^{85} - 234 q^{86} - 576 q^{87} + 42 q^{88} - 348 q^{89} - 288 q^{90} - 30 q^{91} - 132 q^{92} - 252 q^{93} + 36 q^{94} - 168 q^{95} - 36 q^{96} + 30 q^{97} - 66 q^{98} - 36 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1134))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1134.2.a $$\chi_{1134}(1, \cdot)$$ 1134.2.a.a 1 1
1134.2.a.b 1
1134.2.a.c 1
1134.2.a.d 1
1134.2.a.e 1
1134.2.a.f 1
1134.2.a.g 1
1134.2.a.h 1
1134.2.a.i 2
1134.2.a.j 2
1134.2.a.k 2
1134.2.a.l 2
1134.2.a.m 2
1134.2.a.n 2
1134.2.a.o 2
1134.2.a.p 2
1134.2.d $$\chi_{1134}(1133, \cdot)$$ 1134.2.d.a 16 1
1134.2.d.b 16
1134.2.e $$\chi_{1134}(865, \cdot)$$ 1134.2.e.a 2 2
1134.2.e.b 2
1134.2.e.c 2
1134.2.e.d 2
1134.2.e.e 2
1134.2.e.f 2
1134.2.e.g 2
1134.2.e.h 2
1134.2.e.i 2
1134.2.e.j 2
1134.2.e.k 2
1134.2.e.l 2
1134.2.e.m 2
1134.2.e.n 2
1134.2.e.o 2
1134.2.e.p 2
1134.2.e.q 4
1134.2.e.r 4
1134.2.e.s 4
1134.2.e.t 4
1134.2.e.u 8
1134.2.e.v 8
1134.2.f $$\chi_{1134}(379, \cdot)$$ 1134.2.f.a 2 2
1134.2.f.b 2
1134.2.f.c 2
1134.2.f.d 2
1134.2.f.e 2
1134.2.f.f 2
1134.2.f.g 2
1134.2.f.h 2
1134.2.f.i 2
1134.2.f.j 2
1134.2.f.k 2
1134.2.f.l 2
1134.2.f.m 2
1134.2.f.n 2
1134.2.f.o 2
1134.2.f.p 2
1134.2.f.q 4
1134.2.f.r 4
1134.2.f.s 4
1134.2.f.t 4
1134.2.g $$\chi_{1134}(163, \cdot)$$ 1134.2.g.a 2 2
1134.2.g.b 2
1134.2.g.c 2
1134.2.g.d 2
1134.2.g.e 2
1134.2.g.f 2
1134.2.g.g 2
1134.2.g.h 2
1134.2.g.i 4
1134.2.g.j 4
1134.2.g.k 6
1134.2.g.l 6
1134.2.g.m 6
1134.2.g.n 6
1134.2.g.o 8
1134.2.g.p 8
1134.2.h $$\chi_{1134}(109, \cdot)$$ 1134.2.h.a 2 2
1134.2.h.b 2
1134.2.h.c 2
1134.2.h.d 2
1134.2.h.e 2
1134.2.h.f 2
1134.2.h.g 2
1134.2.h.h 2
1134.2.h.i 2
1134.2.h.j 2
1134.2.h.k 2
1134.2.h.l 2
1134.2.h.m 2
1134.2.h.n 2
1134.2.h.o 2
1134.2.h.p 2
1134.2.h.q 4
1134.2.h.r 4
1134.2.h.s 4
1134.2.h.t 4
1134.2.h.u 8
1134.2.h.v 8
1134.2.k $$\chi_{1134}(647, \cdot)$$ 1134.2.k.a 16 2
1134.2.k.b 16
1134.2.k.c 16
1134.2.k.d 16
1134.2.l $$\chi_{1134}(215, \cdot)$$ 1134.2.l.a 4 2
1134.2.l.b 4
1134.2.l.c 4
1134.2.l.d 4
1134.2.l.e 8
1134.2.l.f 8
1134.2.l.g 16
1134.2.l.h 16
1134.2.m $$\chi_{1134}(377, \cdot)$$ 1134.2.m.a 4 2
1134.2.m.b 4
1134.2.m.c 4
1134.2.m.d 4
1134.2.m.e 4
1134.2.m.f 4
1134.2.m.g 8
1134.2.m.h 16
1134.2.m.i 16
1134.2.t $$\chi_{1134}(593, \cdot)$$ 1134.2.t.a 4 2
1134.2.t.b 4
1134.2.t.c 4
1134.2.t.d 4
1134.2.t.e 8
1134.2.t.f 8
1134.2.t.g 16
1134.2.t.h 16
1134.2.u $$\chi_{1134}(127, \cdot)$$ n/a 108 6
1134.2.v $$\chi_{1134}(289, \cdot)$$ n/a 144 6
1134.2.w $$\chi_{1134}(37, \cdot)$$ n/a 144 6
1134.2.z $$\chi_{1134}(125, \cdot)$$ n/a 144 6
1134.2.ba $$\chi_{1134}(17, \cdot)$$ n/a 144 6
1134.2.bf $$\chi_{1134}(143, \cdot)$$ n/a 144 6
1134.2.bg $$\chi_{1134}(67, \cdot)$$ n/a 1296 18
1134.2.bh $$\chi_{1134}(43, \cdot)$$ n/a 972 18
1134.2.bi $$\chi_{1134}(25, \cdot)$$ n/a 1296 18
1134.2.bk $$\chi_{1134}(5, \cdot)$$ n/a 1296 18
1134.2.bp $$\chi_{1134}(47, \cdot)$$ n/a 1296 18
1134.2.bq $$\chi_{1134}(41, \cdot)$$ n/a 1296 18

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1134))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1134)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(378))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(567))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1134))$$$$^{\oplus 1}$$