Properties

Label 9.3.d
Level 9
Weight 3
Character orbit d
Rep. character \(\chi_{9}(2,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 9.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(9, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 6q^{21} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut 48q^{23} \) \(\mathstrut -\mathstrut 45q^{24} \) \(\mathstrut -\mathstrut 13q^{25} \) \(\mathstrut +\mathstrut 54q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 78q^{29} \) \(\mathstrut +\mathstrut 18q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut 27q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 9q^{36} \) \(\mathstrut -\mathstrut 68q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut +\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 54q^{45} \) \(\mathstrut +\mathstrut 96q^{46} \) \(\mathstrut -\mathstrut 84q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 45q^{49} \) \(\mathstrut +\mathstrut 39q^{50} \) \(\mathstrut +\mathstrut 81q^{51} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut -\mathstrut 81q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 30q^{56} \) \(\mathstrut -\mathstrut 33q^{57} \) \(\mathstrut -\mathstrut 78q^{58} \) \(\mathstrut +\mathstrut 87q^{59} \) \(\mathstrut +\mathstrut 18q^{60} \) \(\mathstrut -\mathstrut 56q^{61} \) \(\mathstrut +\mathstrut 36q^{63} \) \(\mathstrut -\mathstrut 142q^{64} \) \(\mathstrut +\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 31q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 135q^{72} \) \(\mathstrut +\mathstrut 130q^{73} \) \(\mathstrut +\mathstrut 102q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 11q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 36q^{78} \) \(\mathstrut -\mathstrut 38q^{79} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut +\mathstrut 42q^{82} \) \(\mathstrut -\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 54q^{85} \) \(\mathstrut -\mathstrut 183q^{86} \) \(\mathstrut -\mathstrut 234q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 54q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 192q^{93} \) \(\mathstrut +\mathstrut 84q^{94} \) \(\mathstrut +\mathstrut 66q^{95} \) \(\mathstrut +\mathstrut 115q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(9, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.3.d.a \(2\) \(0.245\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(6\) \(-2\) \(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)