Properties

Label 18.3.b
Level $18$
Weight $3$
Character orbit 18.b
Rep. character $\chi_{18}(17,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 18.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(18, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\( 2q - 4q^{4} - 8q^{7} + O(q^{10}) \) \( 2q - 4q^{4} - 8q^{7} + 12q^{10} + 16q^{13} + 8q^{16} - 32q^{19} - 48q^{22} + 14q^{25} + 16q^{28} + 88q^{31} + 36q^{34} - 68q^{37} - 24q^{40} - 80q^{43} + 48q^{46} - 66q^{49} - 32q^{52} + 144q^{55} - 12q^{58} + 100q^{61} - 16q^{64} + 16q^{67} - 48q^{70} - 32q^{73} + 64q^{76} - 152q^{79} - 132q^{82} - 108q^{85} + 96q^{88} - 64q^{91} + 240q^{94} + 352q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
18.3.b.a \(2\) \(0.490\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)