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Properties

Label 23.9
Level 23
Weight 9
Dimension 165
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 396
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(396\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(23))\).

Total New Old
Modular forms 187 187 0
Cusp forms 165 165 0
Eisenstein series 22 22 0

Trace form

\( 165 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10}) \) \( 165 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} - 130218 q^{15} - 261899 q^{16} + 246004 q^{17} + 872949 q^{18} - 113894 q^{19} - 1571339 q^{20} - 1081058 q^{21} + 957319 q^{23} + 4553450 q^{24} + 1166275 q^{25} - 177419 q^{26} - 2952356 q^{27} - 6167051 q^{28} - 1109504 q^{29} + 2511861 q^{30} + 2936230 q^{31} + 5955829 q^{32} - 5636796 q^{33} + 6374511 q^{34} - 10230011 q^{35} - 11186516 q^{36} + 9285749 q^{37} + 22442794 q^{38} + 14170453 q^{39} + 4234989 q^{40} - 5773163 q^{41} - 51900761 q^{42} - 21835627 q^{43} - 24763398 q^{44} + 32424381 q^{46} + 29161418 q^{47} + 68005421 q^{48} + 41607445 q^{49} + 18046864 q^{50} - 14740715 q^{51} - 100920061 q^{52} - 28488779 q^{53} - 57299715 q^{54} - 69529317 q^{55} - 99295328 q^{56} + 72285400 q^{57} + 194073374 q^{58} + 103041697 q^{59} + 67737659 q^{60} + 47508681 q^{61} - 1951499 q^{62} - 62854836 q^{63} - 171573259 q^{64} - 173044652 q^{65} - 172762656 q^{66} - 25488397 q^{67} + 69676134 q^{69} + 208147434 q^{70} + 166935604 q^{71} + 406513162 q^{72} + 53013719 q^{73} + 329575444 q^{74} - 58151258 q^{75} - 610693402 q^{76} - 497077394 q^{77} - 556884141 q^{78} - 108193503 q^{79} + 214101118 q^{80} + 811655801 q^{81} + 568273695 q^{82} + 421863970 q^{83} + 585479675 q^{84} - 297208417 q^{85} - 1051470365 q^{86} - 819724235 q^{87} - 546014403 q^{88} - 331520123 q^{89} - 592624846 q^{90} + 300035626 q^{92} + 760407626 q^{93} + 763896320 q^{94} + 1148773186 q^{95} + 1544287096 q^{96} - 137375018 q^{97} - 441866579 q^{98} - 653311670 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(23))\)

We only show spaces with odd 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
23.9.b \(\chi_{23}(22, \cdot)\) 23.9.b.a 3 1
23.9.b.b 12
23.9.d \(\chi_{23}(5, \cdot)\) 23.9.d.a 150 10