Properties

Label 296.2.s
Level $296$
Weight $2$
Character orbit 296.s
Rep. character $\chi_{296}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $1$
Sturm bound $76$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 296 = 2^{3} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 296.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 296 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(76\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(296, [\chi])\).

Total New Old
Modular forms 80 80 0
Cusp forms 72 72 0
Eisenstein series 8 8 0

Trace form

\( 72 q - 2 q^{4} - 8 q^{6} - 6 q^{7} + 30 q^{9} - 8 q^{10} - 2 q^{12} - 8 q^{14} - 14 q^{15} - 6 q^{16} + 18 q^{18} - 16 q^{20} + 8 q^{22} + 20 q^{24} + 24 q^{25} + 8 q^{26} + 4 q^{28} + 4 q^{30} - 8 q^{31}+ \cdots - 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(296, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
296.2.s.a 296.s 296.s $72$ $2.364$ None 296.2.s.a \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$