Properties

Label 9.4.c
Level $9$
Weight $4$
Character orbit 9.c
Rep. character $\chi_{9}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(9, [\chi])\).

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

Trace form

\( 4q - 3q^{2} - 3q^{3} - 5q^{4} - 15q^{5} + 9q^{6} - 7q^{7} + 66q^{8} + 45q^{9} + O(q^{10}) \) \( 4q - 3q^{2} - 3q^{3} - 5q^{4} - 15q^{5} + 9q^{6} - 7q^{7} + 66q^{8} + 45q^{9} + 12q^{10} - 66q^{11} - 156q^{12} + 11q^{13} - 60q^{14} + 27q^{15} + 7q^{16} + 198q^{17} + 216q^{18} - 154q^{19} + 12q^{20} + 21q^{21} + 33q^{22} - 33q^{23} - 99q^{24} + 121q^{25} - 528q^{26} - 432q^{27} + 332q^{28} + 51q^{29} + 288q^{30} - 43q^{31} + 423q^{32} + 198q^{33} - 297q^{34} + 6q^{35} - 225q^{36} - 100q^{37} + 561q^{38} + 759q^{39} - 264q^{40} - 132q^{41} - 486q^{42} - 88q^{43} - 462q^{44} - 675q^{45} - 528q^{46} - 399q^{47} - 21q^{48} + 513q^{49} + 429q^{50} + 297q^{51} + 770q^{52} + 108q^{53} + 1215q^{54} + 1254q^{55} - 66q^{56} - 1221q^{57} + 60q^{58} - 798q^{59} - 36q^{60} - 439q^{61} + 228q^{62} + 603q^{63} - 1454q^{64} - 165q^{65} - 990q^{66} - 988q^{67} - 693q^{68} + 891q^{69} - 318q^{70} + 2736q^{71} + 891q^{72} - 910q^{73} - 816q^{74} - 363q^{75} + 1529q^{76} + 165q^{77} - 990q^{78} + 803q^{79} + 192q^{80} - 567q^{81} + 3630q^{82} - 813q^{83} + 642q^{84} - 594q^{85} - 33q^{86} - 153q^{87} - 1221q^{88} - 792q^{89} - 756q^{90} - 1562q^{91} + 858q^{92} - 213q^{93} - 2100q^{94} + 132q^{95} + 1080q^{96} - 736q^{97} - 846q^{98} + 297q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.4.c.a \(4\) \(0.531\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-3\) \(-3\) \(-15\) \(-7\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)