Properties

Label 189.2.be
Level 189
Weight 2
Character orbit be
Rep. character \(\chi_{189}(20,\cdot)\)
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.be (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

\( 132q - 12q^{2} - 12q^{4} - 6q^{7} - 18q^{8} - 6q^{9} + O(q^{10}) \) \( 132q - 12q^{2} - 12q^{4} - 6q^{7} - 18q^{8} - 6q^{9} - 18q^{11} + 3q^{14} - 24q^{15} - 24q^{16} - 12q^{18} - 12q^{21} - 12q^{22} + 12q^{23} - 12q^{25} - 12q^{28} - 48q^{29} + 42q^{30} - 6q^{32} - 36q^{35} - 36q^{36} - 6q^{37} - 18q^{39} - 12q^{43} - 18q^{44} - 6q^{46} - 24q^{49} + 18q^{50} + 24q^{51} + 57q^{56} - 12q^{58} - 6q^{60} + 21q^{63} + 18q^{64} + 78q^{65} - 12q^{67} - 69q^{70} + 18q^{71} + 114q^{72} - 6q^{74} - 57q^{77} + 12q^{78} + 24q^{79} - 42q^{81} - 48q^{84} + 54q^{85} - 42q^{86} - 72q^{88} + 6q^{91} - 120q^{92} - 60q^{93} + 126q^{95} + 126q^{98} - 192q^{99} + O(q^{100}) \)

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.be.a \(132\) \(1.509\) None \(-12\) \(0\) \(0\) \(-6\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database