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Properties

Label 18.5
Level 18
Weight 5
Dimension 8
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 90
Trace bound 0

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(18))\).

Total New Old
Modular forms 44 8 36
Cusp forms 28 8 20
Eisenstein series 16 0 16

Trace form

\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22} + 1278 q^{23} + 384 q^{24} + 794 q^{25} - 1296 q^{27} - 416 q^{28} - 1854 q^{29} - 3456 q^{30} - 1478 q^{31} - 3384 q^{33} - 96 q^{34} + 1056 q^{36} - 32 q^{37} + 6768 q^{38} + 5274 q^{39} - 36 q^{41} + 2592 q^{42} - 68 q^{43} + 3402 q^{45} + 2112 q^{46} + 2214 q^{47} - 1536 q^{48} + 2442 q^{49} - 15552 q^{50} - 12006 q^{51} - 80 q^{52} + 7056 q^{54} - 3996 q^{55} + 2304 q^{56} + 10902 q^{57} - 2400 q^{58} + 9108 q^{59} + 6480 q^{60} - 4478 q^{61} - 6654 q^{63} - 4096 q^{64} - 22554 q^{65} - 19872 q^{66} + 7504 q^{67} - 11088 q^{68} - 5994 q^{69} + 6048 q^{70} + 5376 q^{72} + 20716 q^{73} + 15264 q^{74} + 16590 q^{75} + 400 q^{76} + 34434 q^{77} + 24096 q^{78} - 6050 q^{79} - 21150 q^{81} + 1152 q^{82} - 3834 q^{83} - 9600 q^{84} - 16092 q^{85} - 12528 q^{86} + 10170 q^{87} - 2688 q^{88} + 2592 q^{90} - 45868 q^{91} + 10224 q^{92} - 10926 q^{93} + 672 q^{94} + 20880 q^{95} + 31336 q^{97} - 22338 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
18.5.b \(\chi_{18}(17, \cdot)\) None 0 1
18.5.d \(\chi_{18}(5, \cdot)\) 18.5.d.a 8 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)