Properties

Label 96.9.e
Level $96$
Weight $9$
Character orbit 96.e
Rep. character $\chi_{96}(65,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $144$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 96.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(9\)
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 32 104
Cusp forms 120 32 88
Eisenstein series 16 0 16

Trace form

\( 32 q - 3808 q^{9} + O(q^{10}) \) \( 32 q - 3808 q^{9} - 51392 q^{13} - 341696 q^{21} - 1862624 q^{25} + 3868928 q^{33} + 9131840 q^{37} + 16972288 q^{45} + 19518560 q^{49} - 8093888 q^{57} + 8197952 q^{61} - 2496000 q^{69} + 79043136 q^{73} + 66121760 q^{81} + 149838848 q^{85} - 78466240 q^{93} + 63367744 q^{97} + O(q^{100}) \)

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.e.a 96.e 3.b $16$ $39.108$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-3\beta _{2})q^{7}+(-435+\cdots)q^{9}+\cdots\)
96.9.e.b 96.e 3.b $16$ $39.108$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)

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

\( S_{9}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)