Properties

Label 18.3.b
Level 18
Weight 3
Character orbit b
Rep. character \(\chi_{18}(17,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(18, [\chi])\) into irreducible Hecke orbits

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 \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)