Properties

Label 189.2.ba
Level 189
Weight 2
Character orbit ba
Rep. character \(\chi_{189}(5,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 132
Newform subspaces 1
Sturm bound 48
Trace bound 0

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Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.ba (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

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

Trace form

\( 132q - 3q^{2} - 9q^{3} - 3q^{4} - 9q^{5} - 18q^{6} - 6q^{7} - 18q^{8} + 3q^{9} + O(q^{10}) \) \( 132q - 3q^{2} - 9q^{3} - 3q^{4} - 9q^{5} - 18q^{6} - 6q^{7} - 18q^{8} + 3q^{9} - 9q^{11} - 9q^{12} + 3q^{14} - 24q^{15} + 3q^{16} - 18q^{17} - 3q^{18} + 18q^{20} - 21q^{21} - 12q^{22} - 6q^{23} - 9q^{24} - 3q^{25} - 12q^{28} + 6q^{29} + 51q^{30} - 9q^{31} + 3q^{32} - 9q^{33} - 18q^{34} + 18q^{35} + 3q^{37} - 99q^{38} - 36q^{39} - 54q^{40} - 45q^{42} - 12q^{43} - 9q^{44} - 9q^{45} + 3q^{46} + 45q^{47} - 24q^{49} - 9q^{50} - 48q^{51} - 9q^{52} - 45q^{53} + 171q^{54} + 3q^{56} - 3q^{58} + 36q^{59} + 57q^{60} - 9q^{61} - 99q^{62} - 33q^{63} + 18q^{64} + 69q^{65} - 9q^{66} - 3q^{67} + 36q^{68} + 108q^{69} + 66q^{70} + 18q^{71} - 129q^{72} - 9q^{73} + 75q^{74} + 36q^{75} + 36q^{76} + 15q^{77} + 66q^{78} - 21q^{79} + 72q^{80} - 33q^{81} - 18q^{82} - 90q^{83} - 120q^{84} + 9q^{85} - 105q^{86} - 54q^{87} - 63q^{88} - 18q^{89} + 81q^{90} + 6q^{91} + 150q^{92} + 21q^{93} - 9q^{94} + 45q^{95} - 81q^{96} + 27q^{98} + 96q^{99} + O(q^{100}) \)

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.ba.a \(132\) \(1.509\) None \(-3\) \(-9\) \(-9\) \(-6\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database