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Properties

Label 9.5.b
Level $9$
Weight $5$
Character orbit 9.b
Rep. character $\chi_{9}(8,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.5.b.a 9.b 3.b $2$ $0.930$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-56\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)