Properties

Label 96.9.g
Level $96$
Weight $9$
Character orbit 96.g
Rep. character $\chi_{96}(31,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 96.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

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

\( 16 q - 672 q^{5} - 34992 q^{9} + O(q^{10}) \) \( 16 q - 672 q^{5} - 34992 q^{9} - 108512 q^{13} + 231840 q^{17} - 243648 q^{21} + 1675056 q^{25} - 137760 q^{29} - 1840320 q^{33} - 3078240 q^{37} - 232032 q^{41} + 1469664 q^{45} - 13579248 q^{49} + 28130784 q^{53} + 1550016 q^{57} + 10550944 q^{61} + 13301952 q^{65} + 2829600 q^{73} - 230503680 q^{77} + 76527504 q^{81} + 82126272 q^{85} - 109134816 q^{89} - 40212288 q^{93} + 300477472 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.9.g.a 96.g 4.b $8$ $39.108$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 96.9.g.a \(0\) \(0\) \(-1232\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-154+\beta _{6})q^{5}+(17\beta _{1}+\cdots)q^{7}+\cdots\)
96.9.g.b 96.g 4.b $8$ $39.108$ 8.0.3468738816.6 None 96.9.g.b \(0\) \(0\) \(560\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(70+\beta _{4})q^{5}+(-7\beta _{1}-7\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{9}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)