Properties

Label 7.9.d
Level 7
Weight 9
Character orbit d
Rep. character \(\chi_{7}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 8
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 9 \)
Character orbit: \([\chi]\) = 7.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(7, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\( 8q - 4q^{2} - 84q^{3} - 164q^{4} - 840q^{5} - 140q^{7} + 6544q^{8} + 396q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 84q^{3} - 164q^{4} - 840q^{5} - 140q^{7} + 6544q^{8} + 396q^{9} + 5796q^{10} + 1784q^{11} - 40908q^{12} - 9856q^{14} + 131808q^{15} - 8584q^{16} - 141456q^{17} - 121944q^{18} - 257544q^{19} + 474012q^{21} + 1706256q^{22} - 348940q^{23} - 895104q^{24} - 557752q^{25} - 2913120q^{26} + 1485092q^{28} + 4983176q^{29} - 551112q^{30} - 2376696q^{31} - 332016q^{32} - 5719140q^{33} + 2491272q^{35} + 13269408q^{36} + 492740q^{37} - 7088088q^{38} - 2850372q^{39} - 7601832q^{40} + 3586128q^{42} + 4448432q^{43} - 3678804q^{44} + 3328164q^{45} - 226560q^{46} + 2704128q^{47} - 3811024q^{49} - 15628912q^{50} - 350856q^{51} + 11135208q^{52} + 2281460q^{53} + 24553368q^{54} - 6573392q^{56} - 43638408q^{57} + 11442696q^{58} + 25291140q^{59} + 17679564q^{60} + 59368764q^{61} - 60081756q^{63} - 114153056q^{64} + 16923396q^{65} + 463428q^{66} - 107108q^{67} + 44316972q^{68} + 19120080q^{70} - 82809760q^{71} + 13297584q^{72} + 116758404q^{73} + 72690340q^{74} + 79832424q^{75} - 58244200q^{77} - 44122512q^{78} - 50628092q^{79} - 93591624q^{80} - 96868872q^{81} - 91061712q^{82} + 154096572q^{84} + 119231208q^{85} + 39093088q^{86} + 26702676q^{87} + 41392848q^{88} - 2322516q^{89} - 151794552q^{91} + 253819128q^{92} - 57693204q^{93} - 345566088q^{94} - 172787052q^{95} - 416455200q^{96} + 373659692q^{98} + 672244008q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.9.d.a \(8\) \(2.852\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-4\) \(-84\) \(-840\) \(-140\) \(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots\)