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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

\( 184 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} - 128 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} + 472 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 440 q^{22} + 496 q^{24} - 8 q^{25} + 260 q^{27} - 8 q^{28}+ \cdots - 5316 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

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