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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

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

Display 100 coefficients 10 coefficients

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 available 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

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