Properties

Label 9.8.c
Level 9
Weight 8
Character orbit c
Rep. character \(\chi_{9}(4,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 12
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 9.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(9, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 12 12 0
Eisenstein series 4 4 0

Trace form

\( 12q - 9q^{2} + 24q^{3} - 321q^{4} - 180q^{5} - 1233q^{6} - 84q^{7} + 5922q^{8} + 990q^{9} + O(q^{10}) \) \( 12q - 9q^{2} + 24q^{3} - 321q^{4} - 180q^{5} - 1233q^{6} - 84q^{7} + 5922q^{8} + 990q^{9} + 252q^{10} - 8460q^{11} + 8052q^{12} - 1848q^{13} - 16272q^{14} - 1188q^{15} - 12417q^{16} + 30564q^{17} + 42876q^{18} + 24432q^{19} - 40788q^{20} - 187224q^{21} - 35001q^{22} - 51588q^{23} + 215469q^{24} + 4746q^{25} + 536472q^{26} + 322272q^{27} + 75516q^{28} - 414648q^{29} - 1112112q^{30} + 8196q^{31} - 1048977q^{32} - 148518q^{33} - 106623q^{34} + 2210616q^{35} + 2501811q^{36} + 139344q^{37} - 1952685q^{38} - 2057316q^{39} + 305496q^{40} - 1731582q^{41} + 538866q^{42} + 408372q^{43} + 5169114q^{44} + 2687580q^{45} - 1684008q^{46} - 1631484q^{47} - 7434525q^{48} - 179010q^{49} - 1654461q^{50} + 2525688q^{51} + 681594q^{52} + 2835648q^{53} + 5816529q^{54} - 16056q^{55} - 1784466q^{56} - 3071850q^{57} - 948384q^{58} - 2055636q^{59} + 371484q^{60} - 2723196q^{61} - 1026828q^{62} - 2238804q^{63} + 7178178q^{64} - 1387620q^{65} + 5754762q^{66} + 3806556q^{67} + 2142639q^{68} - 3002292q^{69} + 953442q^{70} + 2408400q^{71} - 9638325q^{72} - 10670052q^{73} + 9846504q^{74} + 19174632q^{75} - 6727827q^{76} + 3478824q^{77} - 13339962q^{78} + 6020916q^{79} - 38072448q^{80} - 28538730q^{81} + 9403002q^{82} + 9605052q^{83} + 30090090q^{84} - 1698624q^{85} + 34278561q^{86} + 10290708q^{87} - 16459029q^{88} - 24630264q^{89} - 13660596q^{90} + 13570104q^{91} + 39143394q^{92} + 27331212q^{93} + 12602808q^{94} + 10422072q^{95} - 3404376q^{96} + 9977226q^{97} - 95833314q^{98} - 49382676q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.8.c.a \(12\) \(2.811\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-9\) \(24\) \(-180\) \(-84\) \(q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)