Properties

Label 189.2.v
Level 189
Weight 2
Character orbit v
Rep. character \(\chi_{189}(22,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 108
Newform subspaces 2
Sturm bound 48
Trace bound 3

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Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).

Total New Old
Modular forms 156 108 48
Cusp forms 132 108 24
Eisenstein series 24 0 24

Trace form

\( 108q - 6q^{5} - 18q^{8} - 6q^{9} + O(q^{10}) \) \( 108q - 6q^{5} - 18q^{8} - 6q^{9} - 12q^{11} - 36q^{12} - 18q^{15} - 30q^{18} + 6q^{20} - 18q^{22} - 12q^{23} + 72q^{24} - 18q^{25} - 36q^{26} + 6q^{27} + 36q^{29} - 48q^{30} - 18q^{31} + 42q^{32} - 48q^{33} - 18q^{34} - 24q^{35} + 48q^{36} - 24q^{38} - 24q^{39} - 66q^{41} - 30q^{42} - 18q^{43} - 12q^{44} + 42q^{45} - 54q^{47} - 78q^{48} + 144q^{50} + 60q^{51} - 54q^{52} + 72q^{53} - 36q^{54} + 42q^{57} - 54q^{58} + 42q^{59} + 126q^{60} - 54q^{64} + 48q^{65} + 6q^{66} + 18q^{67} + 6q^{68} + 48q^{69} - 72q^{71} + 30q^{72} + 12q^{74} - 24q^{75} + 108q^{76} - 120q^{78} + 36q^{79} - 180q^{80} - 42q^{81} - 30q^{83} - 24q^{84} + 36q^{85} - 24q^{86} - 96q^{87} + 108q^{88} + 48q^{89} + 6q^{90} - 42q^{92} + 114q^{93} - 54q^{94} - 36q^{95} + 144q^{96} - 18q^{97} - 6q^{98} - 66q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.2.v.a \(54\) \(1.509\) None \(0\) \(-3\) \(-3\) \(0\)
189.2.v.b \(54\) \(1.509\) None \(0\) \(3\) \(-3\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database