Properties

Label 7.18
Level 7
Weight 18
Dimension 29
Nonzero newspaces 2
Newforms 3
Sturm bound 72
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(7))\).

Total New Old
Modular forms 37 33 4
Cusp forms 31 29 2
Eisenstein series 6 4 2

Trace form

\( 29q + 1053q^{2} + 2004q^{3} - 33283q^{4} + 2977344q^{5} - 14601606q^{6} + 20160161q^{7} - 187257825q^{8} + 51723873q^{9} + O(q^{10}) \) \( 29q + 1053q^{2} + 2004q^{3} - 33283q^{4} + 2977344q^{5} - 14601606q^{6} + 20160161q^{7} - 187257825q^{8} + 51723873q^{9} - 1016422818q^{10} + 1227799908q^{11} + 4616537898q^{12} - 4327983086q^{13} + 28053317817q^{14} - 16389333888q^{15} + 18546259505q^{16} - 23647570812q^{17} + 24019070739q^{18} - 196028686820q^{19} + 515987762976q^{20} - 663289851798q^{21} + 1333864974996q^{22} - 373760949636q^{23} - 2670251840142q^{24} + 2150181407951q^{25} + 5795376070932q^{26} - 13452646587000q^{27} + 6034546229957q^{28} + 4842057530718q^{29} - 17703498596826q^{30} - 10639475638748q^{31} + 27886828281183q^{32} + 921598162638q^{33} - 23078008853730q^{34} + 7610385236958q^{35} + 112754489779785q^{36} - 31090327243532q^{37} - 17980349540760q^{38} + 98537217720984q^{39} - 86138392110240q^{40} - 184263335072838q^{41} - 165786573778938q^{42} - 75663655735316q^{43} + 728791099364484q^{44} + 79961790311190q^{45} - 1309773898917570q^{46} + 345394818324828q^{47} + 939851741234814q^{48} + 336284765588093q^{49} - 823079729206467q^{50} - 176995814888760q^{51} + 304769573559388q^{52} + 934291175201964q^{53} - 1804543726935774q^{54} - 568345253229168q^{55} - 3199416686864433q^{56} + 3834595152008820q^{57} + 2167302581313330q^{58} + 284460540076260q^{59} + 3080665691959884q^{60} + 5250388540587616q^{61} - 20463533758626264q^{62} + 4450365282921453q^{63} + 12836875769686529q^{64} + 8058264421624704q^{65} + 3083356073840310q^{66} - 3997589427600812q^{67} - 20546925877297134q^{68} - 14428857821848524q^{69} - 14614209554108934q^{70} + 12325433698946664q^{71} + 21867438936271935q^{72} + 952504681479724q^{73} + 31878572405870160q^{74} - 23677625276335452q^{75} - 39274337477946158q^{76} - 45927209832374178q^{77} - 13519274209103712q^{78} + 86040812192268076q^{79} + 157607621746303248q^{80} - 65664343877619393q^{81} - 27851478587558514q^{82} - 3503614324516236q^{83} - 147356539521681294q^{84} - 65572392141325920q^{85} + 168861897027521928q^{86} + 304439903881785480q^{87} + 39599511386685120q^{88} - 165830046534244548q^{89} - 540835012752966564q^{90} - 167206603340010290q^{91} + 142015786974364968q^{92} + 413216353687071018q^{93} + 416852217093436434q^{94} + 248456746691602092q^{95} - 714062885096752926q^{96} - 581608532460020702q^{97} - 734452030668078387q^{98} + 540757598455876860q^{99} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.18.a \(\chi_{7}(1, \cdot)\) 7.18.a.a 4 1
7.18.a.b 5
7.18.c \(\chi_{7}(2, \cdot)\) 7.18.c.a 20 2

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(7))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(7)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)