Properties

Label 96.9.b
Level $96$
Weight $9$
Character orbit 96.b
Rep. character $\chi_{96}(79,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 96.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(96, [\chi])\).

Total New Old
Modular forms 136 16 120
Cusp forms 120 16 104
Eisenstein series 16 0 16

Trace form

\( 16 q + 34992 q^{9} + O(q^{10}) \) \( 16 q + 34992 q^{9} + 39552 q^{11} + 77280 q^{17} - 167552 q^{19} - 1604144 q^{25} + 2415744 q^{35} - 2187360 q^{41} - 3525248 q^{43} - 7109552 q^{49} - 13862016 q^{51} - 1550016 q^{57} - 44938752 q^{59} - 52558464 q^{65} - 6892544 q^{67} + 12400160 q^{73} - 12918528 q^{75} + 76527504 q^{81} + 209328000 q^{83} - 152224800 q^{89} - 395802240 q^{91} - 38799136 q^{97} + 86500224 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.9.b.a 96.b 8.d $16$ $39.108$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+3^{7}q^{9}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)