Properties

Label 867.2
Level 867
Weight 2
Dimension 20297
Nonzero newspaces 10
Newform subspaces 65
Sturm bound 110976
Trace bound 2

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Defining parameters

Level: \( N \) = \( 867 = 3 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 65 \)
Sturm bound: \(110976\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(867))\).

Total New Old
Modular forms 28544 21033 7511
Cusp forms 26945 20297 6648
Eisenstein series 1599 736 863

Trace form

\( 20297q + 3q^{2} - 119q^{3} - 233q^{4} + 6q^{5} - 117q^{6} - 232q^{7} + 15q^{8} - 119q^{9} + O(q^{10}) \) \( 20297q + 3q^{2} - 119q^{3} - 233q^{4} + 6q^{5} - 117q^{6} - 232q^{7} + 15q^{8} - 119q^{9} - 238q^{10} - 20q^{11} - 161q^{12} - 258q^{13} - 40q^{14} - 162q^{15} - 353q^{16} - 16q^{17} - 293q^{18} - 252q^{19} - 70q^{20} - 160q^{21} - 268q^{22} - 8q^{23} - 185q^{24} - 321q^{25} - 102q^{26} - 119q^{27} - 376q^{28} - 50q^{29} - 230q^{30} - 336q^{31} - 97q^{32} - 188q^{33} - 384q^{34} - 80q^{35} - 177q^{36} - 330q^{37} - 100q^{38} - 138q^{39} - 406q^{40} - 38q^{41} - 96q^{42} - 292q^{43} - 44q^{44} - 66q^{45} - 232q^{46} + 48q^{47} + 23q^{48} - 183q^{49} + 93q^{50} - 96q^{51} - 366q^{52} + 6q^{53} - 85q^{54} - 296q^{55} - 40q^{56} - 132q^{57} - 374q^{58} - 68q^{59} - 158q^{60} - 370q^{61} - 128q^{62} - 256q^{63} - 433q^{64} - 156q^{65} - 244q^{66} - 332q^{67} - 200q^{68} - 432q^{69} - 640q^{70} - 120q^{71} - 297q^{72} - 566q^{73} - 222q^{74} - 345q^{75} - 580q^{76} - 224q^{77} - 414q^{78} - 416q^{79} - 358q^{80} - 231q^{81} - 546q^{82} - 140q^{83} - 272q^{84} - 376q^{85} + 4q^{86} - 90q^{87} - 444q^{88} - 6q^{89} + 42q^{90} - 320q^{91} - 152q^{92} - 24q^{93} - 352q^{94} - 8q^{95} + 23q^{96} - 270q^{97} + 27q^{98} - 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)

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
867.2.a \(\chi_{867}(1, \cdot)\) 867.2.a.a 1 1
867.2.a.b 1
867.2.a.c 1
867.2.a.d 1
867.2.a.e 1
867.2.a.f 2
867.2.a.g 2
867.2.a.h 2
867.2.a.i 3
867.2.a.j 3
867.2.a.k 4
867.2.a.l 4
867.2.a.m 4
867.2.a.n 4
867.2.a.o 6
867.2.a.p 6
867.2.d \(\chi_{867}(577, \cdot)\) 867.2.d.a 2 1
867.2.d.b 4
867.2.d.c 4
867.2.d.d 6
867.2.d.e 8
867.2.d.f 8
867.2.d.g 12
867.2.e \(\chi_{867}(616, \cdot)\) 867.2.e.a 4 2
867.2.e.b 4
867.2.e.c 4
867.2.e.d 4
867.2.e.e 4
867.2.e.f 8
867.2.e.g 8
867.2.e.h 8
867.2.e.i 8
867.2.e.j 12
867.2.e.k 24
867.2.h \(\chi_{867}(688, \cdot)\) 867.2.h.a 8 4
867.2.h.b 8
867.2.h.c 8
867.2.h.d 8
867.2.h.e 8
867.2.h.f 8
867.2.h.g 8
867.2.h.h 8
867.2.h.i 16
867.2.h.j 16
867.2.h.k 16
867.2.h.l 24
867.2.h.m 48
867.2.i \(\chi_{867}(65, \cdot)\) 867.2.i.a 16 8
867.2.i.b 32
867.2.i.c 32
867.2.i.d 32
867.2.i.e 32
867.2.i.f 32
867.2.i.g 32
867.2.i.h 32
867.2.i.i 32
867.2.i.j 48
867.2.i.k 96
867.2.i.l 192
867.2.k \(\chi_{867}(52, \cdot)\) 867.2.k.a 416 16
867.2.k.b 416
867.2.l \(\chi_{867}(16, \cdot)\) 867.2.l.a 832 16
867.2.p \(\chi_{867}(4, \cdot)\) 867.2.p.a 1664 32
867.2.q \(\chi_{867}(19, \cdot)\) 867.2.q.a 3200 64
867.2.t \(\chi_{867}(5, \cdot)\) 867.2.t.a 12800 128

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(867))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(867)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)