# Properties

 Label 1122.2 Level 1122 Weight 2 Dimension 8433 Nonzero newspaces 20 Sturm bound 138240 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$1122 = 2 \cdot 3 \cdot 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$138240$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1122))$$.

Total New Old
Modular forms 35840 8433 27407
Cusp forms 33281 8433 24848
Eisenstein series 2559 0 2559

## Trace form

 $$8433q - 3q^{2} - 3q^{3} - 3q^{4} - 18q^{5} + 7q^{6} + 16q^{7} - 3q^{8} + 37q^{9} + O(q^{10})$$ $$8433q - 3q^{2} - 3q^{3} - 3q^{4} - 18q^{5} + 7q^{6} + 16q^{7} - 3q^{8} + 37q^{9} + 38q^{10} + 49q^{11} + 33q^{12} + 62q^{13} + 80q^{14} + 138q^{15} + 13q^{16} + 69q^{17} + 71q^{18} + 64q^{19} - 2q^{20} + 112q^{21} + 9q^{22} + 32q^{23} + 3q^{24} + 131q^{25} - 26q^{26} - 63q^{27} - 24q^{28} + 30q^{29} - 78q^{30} + 72q^{31} - 3q^{32} - 81q^{33} - 35q^{34} + 24q^{35} - 13q^{36} + 14q^{37} - 60q^{38} - 62q^{39} - 18q^{40} - 6q^{41} - 140q^{42} + 84q^{43} + 17q^{44} - 130q^{45} + 8q^{46} + 16q^{47} - 3q^{48} + 69q^{49} - 13q^{50} - 108q^{51} + 38q^{52} - 26q^{53} - 95q^{54} + 94q^{55} - 24q^{56} - 194q^{57} + 70q^{58} + 4q^{59} - 42q^{60} + 78q^{61} + 24q^{62} - 4q^{63} - 3q^{64} + 4q^{65} + 89q^{66} + 60q^{67} + 21q^{68} + 116q^{69} + 144q^{70} + 136q^{71} + 53q^{72} + 274q^{73} + 110q^{74} + 221q^{75} - 20q^{76} + 136q^{77} + 166q^{78} + 200q^{79} + 86q^{80} + 93q^{81} + 166q^{82} + 124q^{83} + 40q^{84} + 250q^{85} + 116q^{86} + 6q^{87} + 81q^{88} + 42q^{89} - 22q^{90} - 32q^{91} - 8q^{92} - 36q^{93} + 32q^{94} + 16q^{95} - 3q^{96} + 22q^{97} - 27q^{98} - 91q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1122))$$

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
1122.2.a $$\chi_{1122}(1, \cdot)$$ 1122.2.a.a 1 1
1122.2.a.b 1
1122.2.a.c 1
1122.2.a.d 1
1122.2.a.e 1
1122.2.a.f 1
1122.2.a.g 1
1122.2.a.h 1
1122.2.a.i 1
1122.2.a.j 1
1122.2.a.k 1
1122.2.a.l 1
1122.2.a.m 1
1122.2.a.n 1
1122.2.a.o 2
1122.2.a.p 2
1122.2.a.q 2
1122.2.a.r 2
1122.2.a.s 3
1122.2.b $$\chi_{1122}(1055, \cdot)$$ 1122.2.b.a 16 1
1122.2.b.b 16
1122.2.b.c 16
1122.2.b.d 16
1122.2.c $$\chi_{1122}(67, \cdot)$$ 1122.2.c.a 2 1
1122.2.c.b 2
1122.2.c.c 2
1122.2.c.d 2
1122.2.c.e 4
1122.2.c.f 4
1122.2.c.g 6
1122.2.c.h 10
1122.2.h $$\chi_{1122}(1121, \cdot)$$ 1122.2.h.a 2 1
1122.2.h.b 2
1122.2.h.c 2
1122.2.h.d 2
1122.2.h.e 4
1122.2.h.f 4
1122.2.h.g 28
1122.2.h.h 28
1122.2.j $$\chi_{1122}(395, \cdot)$$ n/a 144 2
1122.2.l $$\chi_{1122}(463, \cdot)$$ 1122.2.l.a 4 2
1122.2.l.b 4
1122.2.l.c 4
1122.2.l.d 4
1122.2.l.e 12
1122.2.l.f 16
1122.2.l.g 20
1122.2.m $$\chi_{1122}(103, \cdot)$$ n/a 128 4
1122.2.o $$\chi_{1122}(331, \cdot)$$ n/a 112 4
1122.2.q $$\chi_{1122}(263, \cdot)$$ n/a 288 4
1122.2.r $$\chi_{1122}(101, \cdot)$$ n/a 288 4
1122.2.w $$\chi_{1122}(169, \cdot)$$ n/a 144 4
1122.2.x $$\chi_{1122}(35, \cdot)$$ n/a 256 4
1122.2.y $$\chi_{1122}(23, \cdot)$$ n/a 480 8
1122.2.z $$\chi_{1122}(109, \cdot)$$ n/a 288 8
1122.2.bc $$\chi_{1122}(115, \cdot)$$ n/a 288 8
1122.2.be $$\chi_{1122}(149, \cdot)$$ n/a 576 8
1122.2.bg $$\chi_{1122}(83, \cdot)$$ n/a 1152 16
1122.2.bi $$\chi_{1122}(25, \cdot)$$ n/a 576 16
1122.2.bm $$\chi_{1122}(7, \cdot)$$ n/a 1152 32
1122.2.bn $$\chi_{1122}(5, \cdot)$$ n/a 2304 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1122))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1122)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(374))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(561))$$$$^{\oplus 2}$$