Properties

Label 9.6.c
Level $9$
Weight $6$
Character orbit 9.c
Rep. character $\chi_{9}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
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: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(9, [\chi])\).

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

Trace form

\( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9} + O(q^{10}) \) \( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9} + 60 q^{10} + 444 q^{11} + 2724 q^{12} - 182 q^{13} + 1392 q^{14} - 2052 q^{15} - 289 q^{16} - 4356 q^{17} - 8100 q^{18} + 952 q^{19} + 6684 q^{20} + 8670 q^{21} + 1011 q^{22} + 8844 q^{23} + 549 q^{24} - 1654 q^{25} - 24888 q^{26} - 10152 q^{27} - 1604 q^{28} + 12018 q^{29} + 22104 q^{30} + 1132 q^{31} + 8703 q^{32} - 8820 q^{33} + 10125 q^{34} - 16224 q^{35} - 14589 q^{36} - 15176 q^{37} - 11145 q^{38} + 8220 q^{39} - 8736 q^{40} + 1248 q^{41} + 10098 q^{42} - 6092 q^{43} + 49530 q^{44} + 43038 q^{45} + 45960 q^{46} - 60 q^{47} - 57405 q^{48} + 9090 q^{49} - 57057 q^{50} - 9396 q^{51} - 32510 q^{52} + 20952 q^{53} + 8181 q^{54} - 36120 q^{55} - 61170 q^{56} - 104298 q^{57} + 8328 q^{58} + 2076 q^{59} + 88308 q^{60} + 48142 q^{61} + 241764 q^{62} + 133524 q^{63} - 20926 q^{64} - 13146 q^{65} - 100998 q^{66} - 7148 q^{67} - 123129 q^{68} - 125982 q^{69} - 654 q^{70} - 71856 q^{71} + 35451 q^{72} + 122452 q^{73} - 160320 q^{74} - 18732 q^{75} - 49571 q^{76} + 39534 q^{77} + 181422 q^{78} - 59516 q^{79} + 124512 q^{80} + 194562 q^{81} - 233598 q^{82} + 117696 q^{83} + 108354 q^{84} + 28836 q^{85} - 15915 q^{86} - 142956 q^{87} + 104523 q^{88} - 451728 q^{89} - 539892 q^{90} + 111392 q^{91} + 134034 q^{92} + 113898 q^{93} + 169464 q^{94} + 294888 q^{95} + 42768 q^{96} + 33976 q^{97} + 57654 q^{98} + 33696 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.6.c.a 9.c 9.c $8$ $1.443$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(3\) \(-12\) \(78\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)