# Properties

 Label 882.2 Level 882 Weight 2 Dimension 5360 Nonzero newspaces 20 Newform subspaces 129 Sturm bound 84672 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$129$$ Sturm bound: $$84672$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(882))$$.

Total New Old
Modular forms 22128 5360 16768
Cusp forms 20209 5360 14849
Eisenstein series 1919 0 1919

## Trace form

 $$5360 q - q^{2} - 3 q^{3} - 5 q^{4} - 12 q^{5} + 3 q^{6} - 8 q^{7} + 2 q^{8} + 3 q^{9} + O(q^{10})$$ $$5360 q - q^{2} - 3 q^{3} - 5 q^{4} - 12 q^{5} + 3 q^{6} - 8 q^{7} + 2 q^{8} + 3 q^{9} - 12 q^{10} - 21 q^{11} - 6 q^{13} + 18 q^{14} + 48 q^{15} + 11 q^{16} + 90 q^{17} + 42 q^{18} + 66 q^{19} + 36 q^{20} + 36 q^{21} + 75 q^{22} + 102 q^{23} + 21 q^{24} + 65 q^{25} + 64 q^{26} + 72 q^{27} + 42 q^{29} + 24 q^{30} + 12 q^{31} - q^{32} + 39 q^{33} - 21 q^{34} + 30 q^{35} + 3 q^{36} + 64 q^{37} + 7 q^{38} + 72 q^{39} + 30 q^{40} + 171 q^{41} + 77 q^{43} + 12 q^{44} + 96 q^{45} + 66 q^{46} + 162 q^{47} + 3 q^{48} + 186 q^{49} - 31 q^{50} - 63 q^{51} + 32 q^{52} - 36 q^{53} - 135 q^{54} + 210 q^{55} + 36 q^{56} - 189 q^{57} + 126 q^{58} - 147 q^{59} - 144 q^{60} + 134 q^{61} - 134 q^{62} - 168 q^{63} - 2 q^{64} - 336 q^{65} - 192 q^{66} + 67 q^{67} - 117 q^{68} - 216 q^{69} + 18 q^{70} - 168 q^{71} + 3 q^{72} - 18 q^{73} - 140 q^{74} - 183 q^{75} - 3 q^{76} - 72 q^{77} - 102 q^{78} - 20 q^{79} - 12 q^{80} + 15 q^{81} - 54 q^{82} + 60 q^{83} - 36 q^{85} - 23 q^{86} + 162 q^{87} + 27 q^{88} + 216 q^{89} + 96 q^{90} + 142 q^{91} + 54 q^{92} + 216 q^{93} + 78 q^{94} + 456 q^{95} + 24 q^{96} + 207 q^{97} + 96 q^{98} + 258 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$

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
882.2.a $$\chi_{882}(1, \cdot)$$ 882.2.a.a 1 1
882.2.a.b 1
882.2.a.c 1
882.2.a.d 1
882.2.a.e 1
882.2.a.f 1
882.2.a.g 1
882.2.a.h 1
882.2.a.i 1
882.2.a.j 1
882.2.a.k 1
882.2.a.l 1
882.2.a.m 2
882.2.a.n 2
882.2.a.o 2
882.2.d $$\chi_{882}(881, \cdot)$$ 882.2.d.a 8 1
882.2.d.b 8
882.2.e $$\chi_{882}(373, \cdot)$$ 882.2.e.a 2 2
882.2.e.b 2
882.2.e.c 2
882.2.e.d 2
882.2.e.e 2
882.2.e.f 2
882.2.e.g 2
882.2.e.h 2
882.2.e.i 2
882.2.e.j 2
882.2.e.k 4
882.2.e.l 4
882.2.e.m 4
882.2.e.n 4
882.2.e.o 6
882.2.e.p 6
882.2.e.q 8
882.2.e.r 8
882.2.e.s 8
882.2.e.t 8
882.2.f $$\chi_{882}(295, \cdot)$$ 882.2.f.a 2 2
882.2.f.b 2
882.2.f.c 2
882.2.f.d 2
882.2.f.e 2
882.2.f.f 2
882.2.f.g 2
882.2.f.h 2
882.2.f.i 2
882.2.f.j 4
882.2.f.k 4
882.2.f.l 6
882.2.f.m 6
882.2.f.n 6
882.2.f.o 6
882.2.f.p 8
882.2.f.q 8
882.2.f.r 8
882.2.f.s 8
882.2.g $$\chi_{882}(361, \cdot)$$ 882.2.g.a 2 2
882.2.g.b 2
882.2.g.c 2
882.2.g.d 2
882.2.g.e 2
882.2.g.f 2
882.2.g.g 2
882.2.g.h 2
882.2.g.i 2
882.2.g.j 2
882.2.g.k 4
882.2.g.l 4
882.2.g.m 4
882.2.h $$\chi_{882}(67, \cdot)$$ 882.2.h.a 2 2
882.2.h.b 2
882.2.h.c 2
882.2.h.d 2
882.2.h.e 2
882.2.h.f 2
882.2.h.g 2
882.2.h.h 2
882.2.h.i 2
882.2.h.j 2
882.2.h.k 4
882.2.h.l 4
882.2.h.m 4
882.2.h.n 4
882.2.h.o 6
882.2.h.p 6
882.2.h.q 8
882.2.h.r 8
882.2.h.s 8
882.2.h.t 8
882.2.k $$\chi_{882}(215, \cdot)$$ 882.2.k.a 8 2
882.2.k.b 16
882.2.l $$\chi_{882}(227, \cdot)$$ 882.2.l.a 16 2
882.2.l.b 16
882.2.l.c 48
882.2.m $$\chi_{882}(293, \cdot)$$ 882.2.m.a 16 2
882.2.m.b 16
882.2.m.c 48
882.2.t $$\chi_{882}(803, \cdot)$$ 882.2.t.a 16 2
882.2.t.b 16
882.2.t.c 48
882.2.u $$\chi_{882}(127, \cdot)$$ 882.2.u.a 6 6
882.2.u.b 6
882.2.u.c 6
882.2.u.d 12
882.2.u.e 12
882.2.u.f 18
882.2.u.g 18
882.2.u.h 18
882.2.u.i 18
882.2.u.j 18
882.2.v $$\chi_{882}(125, \cdot)$$ 882.2.v.a 96 6
882.2.y $$\chi_{882}(193, \cdot)$$ 882.2.y.a 336 12
882.2.y.b 336
882.2.z $$\chi_{882}(37, \cdot)$$ 882.2.z.a 24 12
882.2.z.b 24
882.2.z.c 24
882.2.z.d 24
882.2.z.e 36
882.2.z.f 36
882.2.z.g 60
882.2.z.h 60
882.2.ba $$\chi_{882}(43, \cdot)$$ 882.2.ba.a 336 12
882.2.ba.b 336
882.2.bb $$\chi_{882}(25, \cdot)$$ 882.2.bb.a 336 12
882.2.bb.b 336
882.2.bc $$\chi_{882}(47, \cdot)$$ 882.2.bc.a 672 12
882.2.bj $$\chi_{882}(41, \cdot)$$ 882.2.bj.a 672 12
882.2.bk $$\chi_{882}(5, \cdot)$$ 882.2.bk.a 672 12
882.2.bl $$\chi_{882}(17, \cdot)$$ 882.2.bl.a 240 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(882))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(882)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 1}$$