Properties

Label 96.2.n
Level $96$
Weight $2$
Character orbit 96.n
Rep. character $\chi_{96}(13,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $32$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 96.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(96, [\chi])\).

Total New Old
Modular forms 72 32 40
Cusp forms 56 32 24
Eisenstein series 16 0 16

Trace form

\( 32 q + O(q^{10}) \) \( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.2.n.a 96.n 32.g $32$ $0.767$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)