Properties

Label 96.4.o
Level $96$
Weight $4$
Character orbit 96.o
Rep. character $\chi_{96}(11,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $184$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 96.o (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(96, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 184 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} - 128 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} + 472 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 440 q^{22} + 496 q^{24} - 8 q^{25} + 260 q^{27} - 8 q^{28} - 1132 q^{30} - 8 q^{33} - 72 q^{34} + 576 q^{36} - 8 q^{37} - 604 q^{39} + 280 q^{40} + 896 q^{42} - 8 q^{43} - 4 q^{45} - 1448 q^{46} - 2448 q^{48} - 112 q^{51} + 784 q^{52} - 224 q^{54} + 280 q^{55} - 4 q^{57} - 368 q^{58} + 2792 q^{60} + 1816 q^{61} - 3032 q^{64} - 3268 q^{66} - 3272 q^{67} - 4 q^{69} - 1016 q^{70} + 1376 q^{72} - 8 q^{73} + 496 q^{75} + 5200 q^{76} + 3316 q^{78} + 5648 q^{79} - 3488 q^{82} + 2408 q^{84} - 1008 q^{85} - 1292 q^{87} + 1552 q^{88} + 2816 q^{90} - 3608 q^{91} + 104 q^{93} - 160 q^{94} + 280 q^{96} - 16 q^{97} - 5316 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.4.o.a 96.o 96.o $184$ $5.664$ None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$