Properties

Label 189.2.bd
Level 189
Weight 2
Character orbit bd
Rep. character \(\chi_{189}(47,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 132
Newforms 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.bd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Newforms: \( 1 \)
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

\(132q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut +\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut +\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 9q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut -\mathstrut 15q^{16} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut -\mathstrut 9q^{19} \) \(\mathstrut -\mathstrut 18q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 30q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut -\mathstrut 3q^{25} \) \(\mathstrut -\mathstrut 12q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut -\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 51q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 9q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 9q^{40} \) \(\mathstrut +\mathstrut 27q^{42} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 63q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 33q^{51} \) \(\mathstrut -\mathstrut 9q^{52} \) \(\mathstrut +\mathstrut 45q^{53} \) \(\mathstrut +\mathstrut 117q^{54} \) \(\mathstrut -\mathstrut 51q^{56} \) \(\mathstrut -\mathstrut 3q^{58} \) \(\mathstrut -\mathstrut 9q^{59} \) \(\mathstrut -\mathstrut 15q^{60} \) \(\mathstrut -\mathstrut 63q^{61} \) \(\mathstrut +\mathstrut 99q^{62} \) \(\mathstrut -\mathstrut 33q^{63} \) \(\mathstrut +\mathstrut 18q^{64} \) \(\mathstrut -\mathstrut 102q^{65} \) \(\mathstrut +\mathstrut 63q^{66} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 144q^{68} \) \(\mathstrut -\mathstrut 108q^{69} \) \(\mathstrut -\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut -\mathstrut 33q^{74} \) \(\mathstrut -\mathstrut 9q^{75} \) \(\mathstrut -\mathstrut 36q^{76} \) \(\mathstrut -\mathstrut 57q^{77} \) \(\mathstrut +\mathstrut 66q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 72q^{80} \) \(\mathstrut +\mathstrut 57q^{81} \) \(\mathstrut -\mathstrut 18q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 51q^{84} \) \(\mathstrut +\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 33q^{86} \) \(\mathstrut -\mathstrut 9q^{87} \) \(\mathstrut +\mathstrut 45q^{88} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut +\mathstrut 150q^{92} \) \(\mathstrut -\mathstrut 87q^{93} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut -\mathstrut 180q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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