Properties

Label 9.5.b
Level 9
Weight 5
Character orbit b
Rep. character \(\chi_{9}(8,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 9.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(9, [\chi])\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\(2q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 56q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 56q^{7} \) \(\mathstrut +\mathstrut 252q^{10} \) \(\mathstrut -\mathstrut 224q^{13} \) \(\mathstrut -\mathstrut 568q^{16} \) \(\mathstrut +\mathstrut 1120q^{19} \) \(\mathstrut -\mathstrut 144q^{22} \) \(\mathstrut -\mathstrut 514q^{25} \) \(\mathstrut +\mathstrut 112q^{28} \) \(\mathstrut -\mathstrut 728q^{31} \) \(\mathstrut +\mathstrut 756q^{34} \) \(\mathstrut -\mathstrut 1652q^{37} \) \(\mathstrut +\mathstrut 3528q^{40} \) \(\mathstrut +\mathstrut 3472q^{43} \) \(\mathstrut -\mathstrut 6768q^{46} \) \(\mathstrut -\mathstrut 3234q^{49} \) \(\mathstrut +\mathstrut 448q^{52} \) \(\mathstrut +\mathstrut 1008q^{55} \) \(\mathstrut +\mathstrut 8388q^{58} \) \(\mathstrut +\mathstrut 5236q^{61} \) \(\mathstrut -\mathstrut 6928q^{64} \) \(\mathstrut -\mathstrut 7568q^{67} \) \(\mathstrut -\mathstrut 7056q^{70} \) \(\mathstrut +\mathstrut 13216q^{73} \) \(\mathstrut -\mathstrut 2240q^{76} \) \(\mathstrut -\mathstrut 8552q^{79} \) \(\mathstrut +\mathstrut 15372q^{82} \) \(\mathstrut -\mathstrut 5292q^{85} \) \(\mathstrut -\mathstrut 2016q^{88} \) \(\mathstrut +\mathstrut 6272q^{91} \) \(\mathstrut +\mathstrut 11088q^{94} \) \(\mathstrut -\mathstrut 11648q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(9, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
9.5.b.a \(2\) \(0.930\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-56\) \(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)