Properties

Label 18.22
Level 18
Weight 22
Dimension 51
Nonzero newspaces 2
Newform subspaces 9
Sturm bound 396
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 9 \)
Sturm bound: \(396\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(18))\).

Total New Old
Modular forms 197 51 146
Cusp forms 181 51 130
Eisenstein series 16 0 16

Trace form

\( 51 q - 2048 q^{2} - 189969 q^{3} - 12582912 q^{4} - 37373712 q^{5} - 256398336 q^{6} + 412335948 q^{7} + 1073741824 q^{8} - 16753337511 q^{9} + O(q^{10}) \) \( 51 q - 2048 q^{2} - 189969 q^{3} - 12582912 q^{4} - 37373712 q^{5} - 256398336 q^{6} + 412335948 q^{7} + 1073741824 q^{8} - 16753337511 q^{9} + 28087547904 q^{10} - 28614561849 q^{11} + 13822328832 q^{12} + 842391850278 q^{13} - 727601281024 q^{14} + 8402046970554 q^{15} - 13194139533312 q^{16} + 275316074004 q^{17} + 22290438162432 q^{18} + 18755545876806 q^{19} - 39189177434112 q^{20} + 117155529406404 q^{21} - 67432119837696 q^{22} - 820973695433184 q^{23} + 76597520498688 q^{24} - 323347806848766 q^{25} - 625510248933376 q^{26} + 2401768548995040 q^{27} - 760645209292800 q^{28} - 2611401575524290 q^{29} + 1431348436058112 q^{30} + 1140855088309122 q^{31} - 2251799813685248 q^{32} + 24205106571969915 q^{33} - 9241852439522304 q^{34} - 2447579935224732 q^{35} - 13921249479622656 q^{36} + 17863437432416358 q^{37} - 46926366987959296 q^{38} - 60069252753431718 q^{39} + 29451928630984704 q^{40} + 75676011878448093 q^{41} - 500519306997178368 q^{42} + 65290404721396449 q^{43} + 432564382130503680 q^{44} + 200003118749552214 q^{45} - 249499631442309120 q^{46} + 1261463962974284028 q^{47} + 194379362139635712 q^{48} - 1505457315056282238 q^{49} - 785770319397005312 q^{50} - 343122041115363789 q^{51} + 883311876797104128 q^{52} + 6104566156470404730 q^{53} - 1185339584401800192 q^{54} - 5365956291526490148 q^{55} - 762945240851021824 q^{56} + 3819352973613445941 q^{57} + 2520229049744523264 q^{58} - 20103107459071148703 q^{59} - 7559827892685766656 q^{60} + 7427361596613977100 q^{61} - 8065459677414645760 q^{62} + 23258513281663507902 q^{63} + 58798996734949195776 q^{64} - 65323614090208482354 q^{65} + 2630434540889751552 q^{66} + 48881747196897179403 q^{67} - 25202447128193925120 q^{68} - 197749148587536177486 q^{69} + 49954067281168183296 q^{70} + 263150400707895396864 q^{71} - 34326675337166979072 q^{72} - 226417028862035260500 q^{73} - 32500810915719596032 q^{74} + 379757730140874236547 q^{75} - 19866387115555160064 q^{76} - 202357855658745905940 q^{77} - 137214895653841483776 q^{78} - 121989755184660693474 q^{79} + 107138240398818803712 q^{80} + 122354709875760458061 q^{81} - 199450738402654556160 q^{82} + 201435595488548126418 q^{83} + 275994137340080553984 q^{84} + 285171849841577109840 q^{85} + 91841469534182970368 q^{86} - 449798081383641825972 q^{87} - 70707702490931920896 q^{88} - 422211582018843189846 q^{89} + 181930994008447279104 q^{90} + 1479352700285448462204 q^{91} - 860853313662546345984 q^{92} - 853572082658853980958 q^{93} + 512740387258102056960 q^{94} + 123863510526668676168 q^{95} + 201594630119985512448 q^{96} - 1553136533628932658651 q^{97} - 2823686922189294812160 q^{98} - 1698071130853072467552 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.22.a \(\chi_{18}(1, \cdot)\) 18.22.a.a 1 1
18.22.a.b 1
18.22.a.c 1
18.22.a.d 1
18.22.a.e 1
18.22.a.f 2
18.22.a.g 2
18.22.c \(\chi_{18}(7, \cdot)\) 18.22.c.a 20 2
18.22.c.b 22

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)