## Defining parameters

 Level: $$N$$ = $$1104 = 2^{4} \cdot 3 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$135168$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1104))$$.

Total New Old
Modular forms 35024 14392 20632
Cusp forms 32561 14012 18549
Eisenstein series 2463 380 2083

## Trace form

 $$14012q - 31q^{3} - 72q^{4} + 4q^{5} - 28q^{6} - 50q^{7} + 24q^{8} - q^{9} + O(q^{10})$$ $$14012q - 31q^{3} - 72q^{4} + 4q^{5} - 28q^{6} - 50q^{7} + 24q^{8} - q^{9} - 72q^{10} + 24q^{11} - 44q^{12} - 90q^{13} - 24q^{14} - 13q^{15} - 120q^{16} - 4q^{17} - 60q^{18} - 34q^{19} - 32q^{20} - 63q^{21} - 120q^{22} - 8q^{23} - 144q^{24} - 40q^{25} - 40q^{26} - 55q^{27} - 88q^{28} + 20q^{29} - 84q^{30} - 98q^{31} - 83q^{33} - 72q^{34} - 48q^{35} - 76q^{36} - 42q^{37} + 16q^{38} - 69q^{39} - 40q^{40} + 12q^{41} + 44q^{42} - 66q^{43} + 80q^{44} - 16q^{45} - 40q^{46} + 84q^{48} - 108q^{49} + 72q^{50} - 101q^{51} - 24q^{52} - 28q^{53} + 52q^{54} - 130q^{55} + 5q^{57} - 120q^{58} - 56q^{59} - 60q^{60} - 218q^{61} + 24q^{62} - 49q^{63} - 216q^{64} + 24q^{65} - 148q^{66} - 98q^{67} - 64q^{68} - 83q^{69} - 320q^{70} + 16q^{71} - 116q^{72} - 82q^{73} - 104q^{74} + 71q^{75} - 216q^{76} + 56q^{77} - 140q^{78} + 98q^{79} - 16q^{80} + 63q^{81} - 136q^{82} + 204q^{83} - 28q^{84} + 130q^{85} + 32q^{86} + 273q^{87} - 24q^{88} + 188q^{89} + 4q^{90} + 304q^{91} + 16q^{92} + 54q^{93} - 8q^{94} + 376q^{95} + 68q^{96} + 46q^{97} + 80q^{98} + 293q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1104))$$

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
1104.2.a $$\chi_{1104}(1, \cdot)$$ 1104.2.a.a 1 1
1104.2.a.b 1
1104.2.a.c 1
1104.2.a.d 1
1104.2.a.e 1
1104.2.a.f 1
1104.2.a.g 1
1104.2.a.h 1
1104.2.a.i 1
1104.2.a.j 2
1104.2.a.k 2
1104.2.a.l 2
1104.2.a.m 2
1104.2.a.n 2
1104.2.a.o 3
1104.2.b $$\chi_{1104}(137, \cdot)$$ None 0 1
1104.2.e $$\chi_{1104}(47, \cdot)$$ 1104.2.e.a 2 1
1104.2.e.b 2
1104.2.e.c 4
1104.2.e.d 4
1104.2.e.e 8
1104.2.e.f 8
1104.2.e.g 8
1104.2.e.h 8
1104.2.f $$\chi_{1104}(553, \cdot)$$ None 0 1
1104.2.i $$\chi_{1104}(367, \cdot)$$ 1104.2.i.a 8 1
1104.2.i.b 16
1104.2.j $$\chi_{1104}(599, \cdot)$$ None 0 1
1104.2.m $$\chi_{1104}(689, \cdot)$$ 1104.2.m.a 6 1
1104.2.m.b 8
1104.2.m.c 8
1104.2.m.d 8
1104.2.m.e 16
1104.2.n $$\chi_{1104}(919, \cdot)$$ None 0 1
1104.2.q $$\chi_{1104}(91, \cdot)$$ n/a 192 2
1104.2.t $$\chi_{1104}(277, \cdot)$$ n/a 176 2
1104.2.u $$\chi_{1104}(323, \cdot)$$ n/a 352 2
1104.2.x $$\chi_{1104}(413, \cdot)$$ n/a 376 2
1104.2.y $$\chi_{1104}(49, \cdot)$$ n/a 240 10
1104.2.bb $$\chi_{1104}(7, \cdot)$$ None 0 10
1104.2.bc $$\chi_{1104}(17, \cdot)$$ n/a 460 10
1104.2.bf $$\chi_{1104}(71, \cdot)$$ None 0 10
1104.2.bg $$\chi_{1104}(79, \cdot)$$ n/a 240 10
1104.2.bj $$\chi_{1104}(25, \cdot)$$ None 0 10
1104.2.bk $$\chi_{1104}(95, \cdot)$$ n/a 480 10
1104.2.bn $$\chi_{1104}(89, \cdot)$$ None 0 10
1104.2.bo $$\chi_{1104}(5, \cdot)$$ n/a 3760 20
1104.2.br $$\chi_{1104}(35, \cdot)$$ n/a 3760 20
1104.2.bs $$\chi_{1104}(13, \cdot)$$ n/a 1920 20
1104.2.bv $$\chi_{1104}(19, \cdot)$$ n/a 1920 20

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1104))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1104)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(368))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(552))$$$$^{\oplus 2}$$