Properties

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

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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

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