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
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.be (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

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

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