Properties

Label 9.6
Level 9
Weight 6
Dimension 9
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 36
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(9))\).

Total New Old
Modular forms 19 14 5
Cusp forms 11 9 2
Eisenstein series 8 5 3

Trace form

\( 9q + 9q^{2} - 12q^{3} - 45q^{4} + 72q^{5} + 171q^{6} - 12q^{7} - 918q^{8} - 414q^{9} + O(q^{10}) \) \( 9q + 9q^{2} - 12q^{3} - 45q^{4} + 72q^{5} + 171q^{6} - 12q^{7} - 918q^{8} - 414q^{9} + 24q^{10} + 1008q^{11} + 2724q^{12} + 456q^{13} + 1152q^{14} - 2052q^{15} - 1425q^{16} - 5238q^{17} - 8100q^{18} + 396q^{19} + 6660q^{20} + 8670q^{21} + 4395q^{22} + 9684q^{23} + 549q^{24} - 4743q^{25} - 21060q^{26} - 10152q^{27} - 1764q^{28} + 7380q^{29} + 22104q^{30} + 5532q^{31} + 7263q^{32} - 8820q^{33} + 4833q^{34} - 15984q^{35} - 14589q^{36} - 17586q^{37} - 14481q^{38} + 8220q^{39} - 7728q^{40} + 8118q^{41} + 10098q^{42} + 3552q^{43} + 51786q^{44} + 43038q^{45} + 51000q^{46} + 18612q^{47} - 57405q^{48} - 6117q^{49} - 75591q^{50} - 9396q^{51} - 29958q^{52} - 12798q^{53} + 8181q^{54} - 39504q^{55} - 54450q^{56} - 104298q^{57} - 19500q^{58} + 20160q^{59} + 88308q^{60} + 87900q^{61} + 268164q^{62} + 133524q^{63} + 6786q^{64} - 16974q^{65} - 100998q^{66} - 30216q^{67} - 126657q^{68} - 125982q^{69} + 786q^{70} - 67608q^{71} + 35451q^{72} + 81342q^{73} - 174780q^{74} - 18732q^{75} - 51795q^{76} + 16974q^{77} + 181422q^{78} - 37596q^{79} + 131328q^{80} + 194562q^{81} - 192378q^{82} + 35244q^{83} + 108354q^{84} + 34128q^{85} + 41949q^{86} - 142956q^{87} + 9771q^{88} - 357642q^{89} - 539892q^{90} + 85872q^{91} + 137394q^{92} + 113898q^{93} + 281496q^{94} + 298224q^{95} + 42768q^{96} + 83418q^{97} - 33588q^{98} + 33696q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.6.a \(\chi_{9}(1, \cdot)\) 9.6.a.a 1 1
9.6.c \(\chi_{9}(4, \cdot)\) 9.6.c.a 8 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)