Properties

Label 7.9
Level 7
Weight 9
Dimension 13
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 36
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(7))\).

Total New Old
Modular forms 19 19 0
Cusp forms 13 13 0
Eisenstein series 6 6 0

Trace form

\( 13 q - 3 q^{2} - 84 q^{3} + 509 q^{4} - 840 q^{5} + 3689 q^{7} - 4047 q^{8} - 1167 q^{9} + O(q^{10}) \) \( 13 q - 3 q^{2} - 84 q^{3} + 509 q^{4} - 840 q^{5} + 3689 q^{7} - 4047 q^{8} - 1167 q^{9} + 5796 q^{10} - 7230 q^{11} - 40908 q^{12} + 14721 q^{14} + 204768 q^{15} + 177145 q^{16} - 141456 q^{17} - 703863 q^{18} - 257544 q^{19} + 1019676 q^{21} + 1071090 q^{22} + 538206 q^{23} - 895104 q^{24} - 2222867 q^{25} - 2913120 q^{26} + 4567717 q^{28} + 3618354 q^{29} + 4161528 q^{30} - 2376696 q^{31} - 9127311 q^{32} - 5719140 q^{33} + 4796232 q^{35} + 12943329 q^{36} + 5134126 q^{37} - 7088088 q^{38} - 12126660 q^{39} - 7601832 q^{40} + 9466128 q^{42} + 3470458 q^{43} + 4971342 q^{44} + 3328164 q^{45} + 3282498 q^{46} + 2704128 q^{47} + 759157 q^{49} - 28706127 q^{50} - 22078728 q^{51} + 11135208 q^{52} + 24408798 q^{53} + 24553368 q^{54} - 50716239 q^{56} - 9904968 q^{57} - 20861910 q^{58} + 25291140 q^{59} + 83159244 q^{60} + 59368764 q^{61} - 84539847 q^{63} - 79570975 q^{64} - 22260924 q^{65} + 463428 q^{66} + 54080678 q^{67} + 44316972 q^{68} - 52239600 q^{70} - 75241014 q^{71} - 42143247 q^{72} + 116758404 q^{73} + 212573958 q^{74} + 79832424 q^{75} - 40531134 q^{77} - 144082512 q^{78} - 197402194 q^{79} - 93591624 q^{80} - 129244419 q^{81} - 91061712 q^{82} + 173966268 q^{84} + 227697768 q^{85} + 421395906 q^{86} + 26702676 q^{87} - 153334926 q^{88} - 2322516 q^{89} + 54362952 q^{91} + 161334138 q^{92} - 148653204 q^{93} - 345566088 q^{94} - 597661932 q^{95} - 416455200 q^{96} + 310463853 q^{98} + 824891058 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.9.b \(\chi_{7}(6, \cdot)\) 7.9.b.a 1 1
7.9.b.b 4
7.9.d \(\chi_{7}(3, \cdot)\) 7.9.d.a 8 2