Properties

Label 18.3
Level 18
Weight 3
Dimension 6
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 54
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(18))\).

Total New Old
Modular forms 26 6 20
Cusp forms 10 6 4
Eisenstein series 16 0 16

Trace form

\( 6 q - 18 q^{5} - 12 q^{6} - 6 q^{7} + 12 q^{9} + O(q^{10}) \) \( 6 q - 18 q^{5} - 12 q^{6} - 6 q^{7} + 12 q^{9} + 12 q^{10} + 18 q^{11} + 12 q^{12} + 6 q^{13} + 36 q^{14} + 18 q^{15} - 24 q^{18} - 72 q^{19} - 36 q^{20} - 42 q^{21} - 60 q^{22} + 18 q^{23} + 18 q^{25} + 24 q^{28} + 18 q^{29} + 72 q^{30} + 126 q^{31} + 54 q^{33} + 60 q^{34} + 12 q^{36} + 60 q^{37} - 72 q^{38} - 102 q^{39} - 24 q^{40} - 126 q^{41} - 48 q^{42} - 126 q^{43} - 54 q^{45} + 24 q^{46} + 54 q^{47} + 24 q^{48} - 78 q^{49} - 72 q^{51} - 12 q^{52} + 36 q^{54} + 36 q^{55} + 72 q^{56} + 144 q^{57} + 12 q^{58} + 126 q^{59} - 36 q^{60} + 162 q^{61} + 222 q^{63} - 48 q^{64} + 90 q^{65} - 72 q^{66} - 90 q^{67} + 72 q^{68} + 18 q^{69} - 156 q^{70} - 96 q^{72} - 240 q^{73} + 72 q^{74} - 12 q^{75} + 24 q^{76} - 90 q^{77} + 144 q^{78} - 138 q^{79} - 252 q^{81} + 12 q^{82} - 378 q^{83} - 144 q^{84} - 108 q^{86} - 54 q^{87} + 120 q^{88} + 348 q^{91} + 36 q^{92} + 222 q^{93} + 324 q^{94} + 180 q^{95} + 48 q^{96} + 366 q^{97} + 126 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
18.3.b \(\chi_{18}(17, \cdot)\) 18.3.b.a 2 1
18.3.d \(\chi_{18}(5, \cdot)\) 18.3.d.a 4 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

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