Properties

Label 7.6
Level 7
Weight 6
Dimension 7
Nonzero newspaces 2
Newforms 3
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(7))\).

Total New Old
Modular forms 13 11 2
Cusp forms 7 7 0
Eisenstein series 6 4 2

Trace form

\( 7q - 3q^{2} - 12q^{3} + 61q^{4} - 36q^{5} - 222q^{6} - 119q^{7} - 177q^{8} + 891q^{9} + O(q^{10}) \) \( 7q - 3q^{2} - 12q^{3} + 61q^{4} - 36q^{5} - 222q^{6} - 119q^{7} - 177q^{8} + 891q^{9} + 1542q^{10} + 204q^{11} - 2310q^{12} - 2338q^{13} - 1743q^{14} + 912q^{15} + 3601q^{16} + 2424q^{17} + 3795q^{18} - 3004q^{19} - 4704q^{20} - 1134q^{21} + 180q^{22} + 3924q^{23} + 1794q^{24} - 5099q^{25} + 2268q^{26} + 3432q^{27} - 539q^{28} - 3990q^{29} - 19866q^{30} - 11212q^{31} - 753q^{32} + 20166q^{33} + 37998q^{34} + 29358q^{35} + 5241q^{36} - 15256q^{37} - 34368q^{38} - 20160q^{39} + 7440q^{40} - 17010q^{41} - 20034q^{42} - 17500q^{43} - 20988q^{44} + 6570q^{45} + 12462q^{46} + 43980q^{47} + 43710q^{48} + 12103q^{49} + 40173q^{50} + 32088q^{51} + 23324q^{52} + 8688q^{53} - 111054q^{54} - 102048q^{55} - 40593q^{56} - 23868q^{57} + 61986q^{58} + 19140q^{59} + 41244q^{60} + 3380q^{61} - 6984q^{62} + 24885q^{63} - 18239q^{64} + 50064q^{65} + 125190q^{66} - 65932q^{67} - 137550q^{68} - 118620q^{69} - 130494q^{70} + 34440q^{71} + 58143q^{72} + 136040q^{73} + 194784q^{74} + 75948q^{75} + 58226q^{76} + 73374q^{77} - 37632q^{78} + 74036q^{79} - 218832q^{80} - 157671q^{81} + 53550q^{82} - 111636q^{83} + 14994q^{84} - 47640q^{85} - 345624q^{86} - 191040q^{87} - 103680q^{88} + 60360q^{89} + 328836q^{90} + 125342q^{91} + 254376q^{92} - 23982q^{93} - 31806q^{94} + 227892q^{95} + 239106q^{96} + 380534q^{97} + 96285q^{98} - 161532q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.6.a \(\chi_{7}(1, \cdot)\) 7.6.a.a 1 1
7.6.a.b 2
7.6.c \(\chi_{7}(2, \cdot)\) 7.6.c.a 4 2