Properties

Label 9.7.b
Level $9$
Weight $7$
Character orbit 9.b
Rep. character $\chi_{9}(8,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
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: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(9, [\chi])\).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

Trace form

\( 2 q - 196 q^{4} + 1048 q^{7} + O(q^{10}) \) \( 2 q - 196 q^{4} + 1048 q^{7} - 1620 q^{10} + 688 q^{13} - 1528 q^{16} - 4640 q^{19} + 22032 q^{22} + 23150 q^{25} - 102704 q^{28} - 21128 q^{31} + 181764 q^{34} - 48164 q^{37} + 55080 q^{40} - 181904 q^{43} - 146448 q^{46} + 313854 q^{49} - 67424 q^{52} + 110160 q^{55} - 589356 q^{58} + 502276 q^{61} + 854768 q^{64} - 432176 q^{67} - 848880 q^{70} - 616352 q^{73} + 454720 q^{76} - 1080248 q^{79} + 2770524 q^{82} + 908820 q^{85} - 749088 q^{88} + 360512 q^{91} - 3282768 q^{94} - 74336 q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.7.b.a 9.b 3.b $2$ $2.070$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(1048\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(9, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(9, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)