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
Newforms 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: \(\Q(\zeta_{9})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into irreducible Hecke orbits

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

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