Properties

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

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
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

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

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