Properties

Label 9.11.b
Level $9$
Weight $11$
Character orbit 9.b
Rep. character $\chi_{9}(8,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 11 \)
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: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(9, [\chi])\).

Total New Old
Modular forms 12 4 8
Cusp forms 8 4 4
Eisenstein series 4 0 4

Trace form

\( 4 q - 4292 q^{4} - 44464 q^{7} - 286020 q^{10} - 173824 q^{13} + 6119944 q^{16} - 965440 q^{19} - 24364656 q^{22} + 10185820 q^{25} - 33121648 q^{28} + 143356304 q^{31} - 87731532 q^{34} + 112531832 q^{37}+ \cdots + 29655344768 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{11}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.11.b.a 9.b 3.b $4$ $5.718$ \(\Q(\sqrt{-2}, \sqrt{385})\) None 9.11.b.a \(0\) \(0\) \(0\) \(-44464\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(9, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(9, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)