Properties

Label 18.6
Level 18
Weight 6
Dimension 13
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 108
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(108\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(18))\).

Total New Old
Modular forms 53 13 40
Cusp forms 37 13 24
Eisenstein series 16 0 16

Trace form

\( 13q - 8q^{2} + 9q^{3} - 32q^{4} - 42q^{5} - 84q^{6} - 178q^{7} + 64q^{8} + 579q^{9} + O(q^{10}) \) \( 13q - 8q^{2} + 9q^{3} - 32q^{4} - 42q^{5} - 84q^{6} - 178q^{7} + 64q^{8} + 579q^{9} + 504q^{10} - 333q^{11} - 384q^{12} - 964q^{13} - 1528q^{14} + 2664q^{15} - 512q^{16} + 4296q^{17} + 2568q^{18} - 1390q^{19} - 672q^{20} - 11310q^{21} - 4260q^{22} - 9306q^{23} + 576q^{24} + 13594q^{25} + 17432q^{26} + 18144q^{27} - 64q^{28} - 14616q^{29} - 7488q^{30} - 16612q^{31} - 2048q^{32} - 405q^{33} - 10092q^{34} + 12048q^{35} - 7440q^{36} + 33482q^{37} - 14908q^{38} - 30432q^{39} + 8064q^{40} + 1209q^{41} + 36960q^{42} - 14959q^{43} + 13536q^{44} + 7884q^{45} + 14160q^{46} + 57558q^{47} + 3840q^{48} + 1950q^{49} - 28712q^{50} - 44379q^{51} - 15424q^{52} - 97446q^{53} - 116604q^{54} - 13608q^{55} - 24448q^{56} + 89667q^{57} + 16512q^{58} + 58581q^{59} + 42624q^{60} - 18442q^{61} + 120992q^{62} + 55788q^{63} + 53248q^{64} + 77856q^{65} + 80064q^{66} + 60275q^{67} - 24432q^{68} - 68292q^{69} - 170064q^{70} - 283488q^{71} - 59712q^{72} - 170020q^{73} - 65224q^{74} - 86403q^{75} + 2192q^{76} + 120762q^{77} + 240840q^{78} + 204836q^{79} + 72192q^{80} + 173007q^{81} + 212976q^{82} + 129864q^{83} - 2016q^{84} - 106380q^{85} - 310252q^{86} - 170046q^{87} - 68160q^{88} + 80274q^{89} - 344736q^{90} - 219656q^{91} - 148896q^{92} - 87780q^{93} + 26760q^{94} + 131568q^{95} + 12288q^{96} + 122189q^{97} + 609732q^{98} + 601794q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.6.a \(\chi_{18}(1, \cdot)\) 18.6.a.a 1 1
18.6.a.b 1
18.6.a.c 1
18.6.c \(\chi_{18}(7, \cdot)\) 18.6.c.a 4 2
18.6.c.b 6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)