# Properties

 Label 1152.4 Level 1152 Weight 4 Dimension 49032 Nonzero newspaces 20 Sturm bound 294912 Trace bound 33

## Defining parameters

 Level: $$N$$ = $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$20$$ Sturm bound: $$294912$$ Trace bound: $$33$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1152))$$.

Total New Old
Modular forms 111872 49464 62408
Cusp forms 109312 49032 60280
Eisenstein series 2560 432 2128

## Trace form

 $$49032 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} + O(q^{10})$$ $$49032 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 64 q^{6} - 36 q^{7} - 48 q^{8} - 80 q^{9} - 144 q^{10} - 36 q^{11} - 64 q^{12} - 48 q^{13} - 48 q^{14} - 48 q^{15} - 48 q^{16} - 72 q^{17} - 64 q^{18} - 108 q^{19} - 48 q^{20} - 64 q^{21} - 48 q^{22} - 364 q^{23} - 64 q^{24} - 236 q^{25} - 48 q^{26} - 48 q^{27} - 144 q^{28} + 352 q^{29} - 64 q^{30} + 712 q^{31} - 48 q^{32} - 128 q^{33} - 48 q^{34} + 420 q^{35} - 64 q^{36} - 128 q^{37} - 48 q^{38} - 48 q^{39} - 48 q^{40} - 1004 q^{41} - 64 q^{42} - 844 q^{43} - 48 q^{44} - 64 q^{45} - 144 q^{46} - 24 q^{47} - 64 q^{48} + 1300 q^{49} + 5664 q^{50} - 48 q^{51} + 6576 q^{52} + 1456 q^{53} - 64 q^{54} + 180 q^{55} - 832 q^{56} - 80 q^{57} - 4800 q^{58} - 1412 q^{59} - 64 q^{60} - 3696 q^{61} - 5904 q^{62} - 48 q^{63} - 12240 q^{64} - 3952 q^{65} - 64 q^{66} - 2076 q^{67} - 4176 q^{68} + 152 q^{69} - 4080 q^{70} - 260 q^{71} - 64 q^{72} + 1548 q^{73} + 5216 q^{74} + 952 q^{75} + 11856 q^{76} + 7876 q^{77} - 64 q^{78} + 11288 q^{79} + 9984 q^{80} + 7264 q^{81} - 144 q^{82} + 7284 q^{83} - 64 q^{84} + 2392 q^{85} - 48 q^{86} - 2624 q^{87} - 48 q^{88} - 10236 q^{89} - 64 q^{90} - 10908 q^{91} - 48 q^{92} - 8608 q^{93} - 48 q^{94} - 18288 q^{95} - 64 q^{96} - 17952 q^{97} - 48 q^{98} - 10672 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1152))$$

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
1152.4.a $$\chi_{1152}(1, \cdot)$$ 1152.4.a.a 1 1
1152.4.a.b 1
1152.4.a.c 1
1152.4.a.d 1
1152.4.a.e 1
1152.4.a.f 1
1152.4.a.g 1
1152.4.a.h 1
1152.4.a.i 1
1152.4.a.j 1
1152.4.a.k 1
1152.4.a.l 1
1152.4.a.m 2
1152.4.a.n 2
1152.4.a.o 2
1152.4.a.p 2
1152.4.a.q 2
1152.4.a.r 2
1152.4.a.s 2
1152.4.a.t 2
1152.4.a.u 2
1152.4.a.v 2
1152.4.a.w 2
1152.4.a.x 2
1152.4.a.y 3
1152.4.a.z 3
1152.4.a.ba 3
1152.4.a.bb 3
1152.4.a.bc 3
1152.4.a.bd 3
1152.4.a.be 3
1152.4.a.bf 3
1152.4.c $$\chi_{1152}(1151, \cdot)$$ 1152.4.c.a 12 1
1152.4.c.b 12
1152.4.c.c 12
1152.4.c.d 12
1152.4.d $$\chi_{1152}(577, \cdot)$$ 1152.4.d.a 2 1
1152.4.d.b 2
1152.4.d.c 2
1152.4.d.d 2
1152.4.d.e 2
1152.4.d.f 2
1152.4.d.g 2
1152.4.d.h 2
1152.4.d.i 4
1152.4.d.j 4
1152.4.d.k 4
1152.4.d.l 4
1152.4.d.m 4
1152.4.d.n 4
1152.4.d.o 4
1152.4.d.p 8
1152.4.d.q 8
1152.4.f $$\chi_{1152}(575, \cdot)$$ 1152.4.f.a 4 1
1152.4.f.b 4
1152.4.f.c 4
1152.4.f.d 4
1152.4.f.e 8
1152.4.f.f 12
1152.4.f.g 12
1152.4.i $$\chi_{1152}(385, \cdot)$$ n/a 288 2
1152.4.k $$\chi_{1152}(289, \cdot)$$ n/a 116 2
1152.4.l $$\chi_{1152}(287, \cdot)$$ 1152.4.l.a 48 2
1152.4.l.b 48
1152.4.p $$\chi_{1152}(191, \cdot)$$ n/a 288 2
1152.4.r $$\chi_{1152}(193, \cdot)$$ n/a 288 2
1152.4.s $$\chi_{1152}(383, \cdot)$$ n/a 288 2
1152.4.v $$\chi_{1152}(145, \cdot)$$ n/a 236 4
1152.4.w $$\chi_{1152}(143, \cdot)$$ n/a 192 4
1152.4.y $$\chi_{1152}(95, \cdot)$$ n/a 560 4
1152.4.bb $$\chi_{1152}(97, \cdot)$$ n/a 560 4
1152.4.bd $$\chi_{1152}(73, \cdot)$$ None 0 8
1152.4.be $$\chi_{1152}(71, \cdot)$$ None 0 8
1152.4.bg $$\chi_{1152}(49, \cdot)$$ n/a 1136 8
1152.4.bj $$\chi_{1152}(47, \cdot)$$ n/a 1136 8
1152.4.bl $$\chi_{1152}(37, \cdot)$$ n/a 3824 16
1152.4.bm $$\chi_{1152}(35, \cdot)$$ n/a 3072 16
1152.4.bp $$\chi_{1152}(23, \cdot)$$ None 0 16
1152.4.bq $$\chi_{1152}(25, \cdot)$$ None 0 16
1152.4.bs $$\chi_{1152}(11, \cdot)$$ n/a 18368 32
1152.4.bv $$\chi_{1152}(13, \cdot)$$ n/a 18368 32

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1152))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1152)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 21}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 14}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 15}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 7}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(384))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(576))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1152))$$$$^{\oplus 1}$$