Properties

Label 96.9.p
Level $96$
Weight $9$
Character orbit 96.p
Rep. character $\chi_{96}(5,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $504$
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.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
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 520 520 0
Cusp forms 504 504 0
Eisenstein series 16 16 0

Trace form

\( 504 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 504 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} - 35008 q^{10} - 4 q^{12} - 8 q^{13} + 445400 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 528072 q^{22} + 161136 q^{24} - 8 q^{25} + 51068 q^{27} - 8 q^{28} + 3966132 q^{30} - 16 q^{31} - 8 q^{33} - 2056 q^{34} + 4835584 q^{36} - 8 q^{37} - 7650052 q^{39} - 15547624 q^{40} - 18128864 q^{42} - 8 q^{43} - 4 q^{45} + 11790680 q^{46} - 21819984 q^{48} - 26248 q^{51} + 12444944 q^{52} + 42722368 q^{54} - 46326792 q^{55} - 4 q^{57} + 39078992 q^{58} - 85332824 q^{60} - 48952072 q^{61} - 8 q^{63} - 48383960 q^{64} - 113022436 q^{66} - 149408776 q^{67} - 4 q^{69} + 46444936 q^{70} + 53585696 q^{72} - 8 q^{73} - 1562504 q^{75} - 139390896 q^{76} + 10120308 q^{78} - 34899808 q^{82} + 688968232 q^{84} - 3125008 q^{85} - 149712644 q^{87} - 22793968 q^{88} - 931912864 q^{90} + 350400760 q^{91} - 26248 q^{93} - 463124896 q^{94} + 710546072 q^{96} - 16 q^{97} - 630017028 q^{99} + O(q^{100}) \)

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.p.a 96.p 96.p $504$ $39.108$ None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$