Properties

Label 9.4.c
Level 9
Weight 4
Character orbit c
Rep. character \(\chi_{9}(4,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(9, [\chi])\) into irreducible Hecke orbits

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 \(-3\) \(-3\) \(-15\) \(-7\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)