Properties

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

Related objects

Downloads

Learn more about

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: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{6}^{\mathrm{new}}(9, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.6.c.a \(8\) \(1.443\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(3\) \(-12\) \(78\) \(28\) \(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)