Properties

Label 18.11
Level 18
Weight 11
Dimension 22
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 198
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(198\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(18))\).

Total New Old
Modular forms 98 22 76
Cusp forms 82 22 60
Eisenstein series 16 0 16

Trace form

\( 22 q - 84 q^{3} + 4096 q^{4} - 9918 q^{5} + 12864 q^{6} + 53510 q^{7} + 79248 q^{9} + O(q^{10}) \) \( 22 q - 84 q^{3} + 4096 q^{4} - 9918 q^{5} + 12864 q^{6} + 53510 q^{7} + 79248 q^{9} + 92352 q^{10} - 327582 q^{11} + 9216 q^{12} + 582506 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2097152 q^{16} + 3925632 q^{18} + 4544768 q^{19} - 5078016 q^{20} - 11895726 q^{21} + 1905984 q^{22} + 10446606 q^{23} + 2752512 q^{24} + 20812198 q^{25} + 2340576 q^{27} - 8599552 q^{28} + 32440806 q^{29} + 37556352 q^{30} - 112013230 q^{31} - 35367930 q^{33} - 78462528 q^{34} - 32695296 q^{36} - 69522628 q^{37} + 370567296 q^{38} + 153125550 q^{39} - 47284224 q^{40} - 245419398 q^{41} - 344505600 q^{42} + 259338986 q^{43} + 394622766 q^{45} - 10714752 q^{46} + 1094979330 q^{47} + 26738688 q^{48} - 311333562 q^{49} - 456606720 q^{50} - 2329772724 q^{51} - 298243072 q^{52} + 1623484224 q^{54} - 121142484 q^{55} + 89948160 q^{56} + 311135772 q^{57} + 1345574592 q^{58} - 2125085130 q^{59} - 2357738496 q^{60} - 2291963914 q^{61} + 5475513858 q^{63} - 2952790016 q^{64} + 13076821350 q^{65} + 2185467264 q^{66} - 4834218154 q^{67} - 2610487296 q^{68} - 11765922354 q^{69} + 3044457024 q^{70} + 1554382848 q^{72} + 9101802536 q^{73} + 9118122624 q^{74} + 13244996208 q^{75} - 4604993536 q^{76} - 33678720774 q^{77} - 14572366080 q^{78} - 7971852238 q^{79} + 14546869128 q^{81} + 8305809600 q^{82} + 16739541378 q^{83} + 1518514176 q^{84} + 16990390440 q^{85} - 11512304064 q^{86} - 32778228834 q^{87} - 975863808 q^{88} + 16769410560 q^{90} + 7383181732 q^{91} + 5348662272 q^{92} - 4843832814 q^{93} - 1161539520 q^{94} - 26494427340 q^{95} - 1962934272 q^{96} + 13517033150 q^{97} + 41160676842 q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.11.b \(\chi_{18}(17, \cdot)\) 18.11.b.a 2 1
18.11.d \(\chi_{18}(5, \cdot)\) 18.11.d.a 20 2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)