# Properties

 Label 864.2 Level 864 Weight 2 Dimension 9056 Nonzero newspaces 18 Newform subspaces 48 Sturm bound 82944 Trace bound 29

## Defining parameters

 Level: $$N$$ = $$864 = 2^{5} \cdot 3^{3}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$48$$ Sturm bound: $$82944$$ Trace bound: $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(864))$$.

Total New Old
Modular forms 21696 9376 12320
Cusp forms 19777 9056 10721
Eisenstein series 1919 320 1599

## Trace form

 $$9056 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 32 q^{5} - 48 q^{6} - 42 q^{7} - 32 q^{8} - 72 q^{9} + O(q^{10})$$ $$9056 q - 32 q^{2} - 36 q^{3} - 56 q^{4} - 32 q^{5} - 48 q^{6} - 42 q^{7} - 32 q^{8} - 72 q^{9} - 56 q^{10} - 26 q^{11} - 48 q^{12} - 56 q^{13} - 32 q^{14} - 36 q^{15} - 56 q^{16} - 24 q^{17} - 48 q^{18} - 50 q^{19} - 32 q^{20} - 48 q^{21} - 56 q^{22} - 34 q^{23} - 48 q^{24} - 100 q^{25} - 32 q^{26} - 36 q^{27} - 128 q^{28} - 48 q^{29} - 48 q^{30} - 50 q^{31} - 32 q^{32} - 120 q^{33} - 56 q^{34} - 14 q^{35} - 48 q^{36} - 40 q^{37} + 24 q^{38} - 36 q^{39} + 8 q^{40} - 16 q^{41} - 48 q^{42} - 26 q^{43} + 56 q^{44} - 48 q^{45} + 8 q^{46} + 6 q^{47} - 48 q^{48} + 4 q^{49} + 72 q^{50} - 18 q^{51} + 8 q^{52} + 16 q^{53} - 48 q^{54} - 60 q^{55} + 48 q^{56} - 48 q^{57} + 8 q^{58} + 46 q^{59} - 48 q^{60} + 24 q^{61} - 24 q^{62} + 24 q^{63} - 56 q^{64} + 100 q^{65} - 48 q^{66} + 22 q^{67} + 48 q^{69} - 56 q^{70} + 106 q^{71} - 48 q^{72} - 36 q^{73} - 32 q^{74} + 48 q^{75} - 56 q^{76} + 128 q^{77} - 48 q^{78} + 62 q^{79} - 96 q^{80} + 72 q^{81} - 208 q^{82} + 174 q^{83} - 48 q^{84} + 8 q^{85} - 136 q^{86} - 136 q^{88} + 24 q^{89} - 48 q^{90} + 106 q^{91} - 184 q^{92} - 48 q^{93} - 184 q^{94} + 170 q^{95} - 48 q^{96} - 108 q^{97} - 152 q^{98} - 36 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(864))$$

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
864.2.a $$\chi_{864}(1, \cdot)$$ 864.2.a.a 1 1
864.2.a.b 1
864.2.a.c 1
864.2.a.d 1
864.2.a.e 1
864.2.a.f 1
864.2.a.g 1
864.2.a.h 1
864.2.a.i 1
864.2.a.j 1
864.2.a.k 1
864.2.a.l 1
864.2.a.m 2
864.2.a.n 2
864.2.c $$\chi_{864}(863, \cdot)$$ 864.2.c.a 8 1
864.2.c.b 8
864.2.d $$\chi_{864}(433, \cdot)$$ 864.2.d.a 4 1
864.2.d.b 4
864.2.d.c 8
864.2.f $$\chi_{864}(431, \cdot)$$ 864.2.f.a 8 1
864.2.f.b 8
864.2.i $$\chi_{864}(289, \cdot)$$ 864.2.i.a 2 2
864.2.i.b 2
864.2.i.c 4
864.2.i.d 4
864.2.i.e 4
864.2.i.f 8
864.2.k $$\chi_{864}(217, \cdot)$$ None 0 2
864.2.l $$\chi_{864}(215, \cdot)$$ None 0 2
864.2.p $$\chi_{864}(143, \cdot)$$ 864.2.p.a 4 2
864.2.p.b 16
864.2.r $$\chi_{864}(145, \cdot)$$ 864.2.r.a 4 2
864.2.r.b 16
864.2.s $$\chi_{864}(287, \cdot)$$ 864.2.s.a 24 2
864.2.v $$\chi_{864}(109, \cdot)$$ 864.2.v.a 128 4
864.2.v.b 128
864.2.w $$\chi_{864}(107, \cdot)$$ 864.2.w.a 128 4
864.2.w.b 128
864.2.y $$\chi_{864}(97, \cdot)$$ 864.2.y.a 48 6
864.2.y.b 54
864.2.y.c 54
864.2.y.d 60
864.2.z $$\chi_{864}(71, \cdot)$$ None 0 4
864.2.bc $$\chi_{864}(73, \cdot)$$ None 0 4
864.2.bf $$\chi_{864}(49, \cdot)$$ 864.2.bf.a 204 6
864.2.bh $$\chi_{864}(47, \cdot)$$ 864.2.bh.a 12 6
864.2.bh.b 192
864.2.bi $$\chi_{864}(95, \cdot)$$ 864.2.bi.a 216 6
864.2.bk $$\chi_{864}(37, \cdot)$$ 864.2.bk.a 368 8
864.2.bn $$\chi_{864}(35, \cdot)$$ 864.2.bn.a 368 8
864.2.bo $$\chi_{864}(25, \cdot)$$ None 0 12
864.2.br $$\chi_{864}(23, \cdot)$$ None 0 12
864.2.bt $$\chi_{864}(11, \cdot)$$ 864.2.bt.a 3408 24
864.2.bu $$\chi_{864}(13, \cdot)$$ 864.2.bu.a 3408 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(864))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(864)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(432))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(864))$$$$^{\oplus 1}$$