# Properties

 Label 1143.2 Level 1143 Weight 2 Dimension 37737 Nonzero newspaces 32 Sturm bound 193536 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$1143 = 3^{2} \cdot 127$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$193536$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1143))$$.

Total New Old
Modular forms 49392 38861 10531
Cusp forms 47377 37737 9640
Eisenstein series 2015 1124 891

## Trace form

 $$37737q - 189q^{2} - 252q^{3} - 189q^{4} - 189q^{5} - 252q^{6} - 189q^{7} - 189q^{8} - 252q^{9} + O(q^{10})$$ $$37737q - 189q^{2} - 252q^{3} - 189q^{4} - 189q^{5} - 252q^{6} - 189q^{7} - 189q^{8} - 252q^{9} - 567q^{10} - 189q^{11} - 252q^{12} - 189q^{13} - 189q^{14} - 252q^{15} - 189q^{16} - 189q^{17} - 252q^{18} - 567q^{19} - 189q^{20} - 252q^{21} - 189q^{22} - 189q^{23} - 252q^{24} - 189q^{25} - 189q^{26} - 252q^{27} - 567q^{28} - 189q^{29} - 252q^{30} - 189q^{31} - 189q^{32} - 252q^{33} - 189q^{34} - 189q^{35} - 252q^{36} - 567q^{37} - 189q^{38} - 252q^{39} - 189q^{40} - 189q^{41} - 252q^{42} - 189q^{43} - 189q^{44} - 252q^{45} - 567q^{46} - 189q^{47} - 252q^{48} - 189q^{49} - 189q^{50} - 252q^{51} - 189q^{52} - 189q^{53} - 252q^{54} - 567q^{55} - 189q^{56} - 252q^{57} - 189q^{58} - 189q^{59} - 252q^{60} - 189q^{61} - 189q^{62} - 252q^{63} - 567q^{64} - 189q^{65} - 252q^{66} - 189q^{67} - 189q^{68} - 252q^{69} - 189q^{70} - 189q^{71} - 252q^{72} - 567q^{73} - 189q^{74} - 252q^{75} - 189q^{76} - 189q^{77} - 252q^{78} - 189q^{79} - 189q^{80} - 252q^{81} - 567q^{82} - 189q^{83} - 252q^{84} - 189q^{85} - 189q^{86} - 252q^{87} - 189q^{88} - 189q^{89} - 252q^{90} - 567q^{91} - 189q^{92} - 252q^{93} - 189q^{94} - 189q^{95} - 252q^{96} - 189q^{97} - 189q^{98} - 252q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1143))$$

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
1143.2.a $$\chi_{1143}(1, \cdot)$$ 1143.2.a.a 1 1
1143.2.a.b 1
1143.2.a.c 1
1143.2.a.d 1
1143.2.a.e 3
1143.2.a.f 4
1143.2.a.g 5
1143.2.a.h 5
1143.2.a.i 7
1143.2.a.j 9
1143.2.a.k 16
1143.2.c $$\chi_{1143}(1142, \cdot)$$ 1143.2.c.a 4 1
1143.2.c.b 20
1143.2.c.c 20
1143.2.e $$\chi_{1143}(382, \cdot)$$ n/a 252 2
1143.2.f $$\chi_{1143}(742, \cdot)$$ n/a 252 2
1143.2.g $$\chi_{1143}(400, \cdot)$$ n/a 252 2
1143.2.h $$\chi_{1143}(19, \cdot)$$ n/a 106 2
1143.2.j $$\chi_{1143}(782, \cdot)$$ 1143.2.j.a 88 2
1143.2.n $$\chi_{1143}(20, \cdot)$$ n/a 252 2
1143.2.o $$\chi_{1143}(362, \cdot)$$ n/a 252 2
1143.2.p $$\chi_{1143}(380, \cdot)$$ n/a 252 2
1143.2.u $$\chi_{1143}(64, \cdot)$$ n/a 318 6
1143.2.v $$\chi_{1143}(22, \cdot)$$ n/a 756 6
1143.2.w $$\chi_{1143}(103, \cdot)$$ n/a 756 6
1143.2.x $$\chi_{1143}(37, \cdot)$$ n/a 312 6
1143.2.z $$\chi_{1143}(125, \cdot)$$ n/a 264 6
1143.2.bb $$\chi_{1143}(278, \cdot)$$ n/a 252 6
1143.2.bg $$\chi_{1143}(59, \cdot)$$ n/a 756 6
1143.2.bi $$\chi_{1143}(329, \cdot)$$ n/a 756 6
1143.2.bk $$\chi_{1143}(73, \cdot)$$ n/a 636 12
1143.2.bl $$\chi_{1143}(61, \cdot)$$ n/a 1512 12
1143.2.bm $$\chi_{1143}(25, \cdot)$$ n/a 1512 12
1143.2.bn $$\chi_{1143}(4, \cdot)$$ n/a 1512 12
1143.2.bs $$\chi_{1143}(95, \cdot)$$ n/a 1512 12
1143.2.bt $$\chi_{1143}(5, \cdot)$$ n/a 1512 12
1143.2.bu $$\chi_{1143}(77, \cdot)$$ n/a 1512 12
1143.2.by $$\chi_{1143}(80, \cdot)$$ n/a 528 12
1143.2.ca $$\chi_{1143}(82, \cdot)$$ n/a 1872 36
1143.2.cb $$\chi_{1143}(13, \cdot)$$ n/a 4536 36
1143.2.cc $$\chi_{1143}(49, \cdot)$$ n/a 4536 36
1143.2.ce $$\chi_{1143}(14, \cdot)$$ n/a 4536 36
1143.2.cg $$\chi_{1143}(56, \cdot)$$ n/a 4536 36
1143.2.cl $$\chi_{1143}(53, \cdot)$$ n/a 1512 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1143))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1143)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(127))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(381))$$$$^{\oplus 2}$$