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Properties

Label 592.2.bj
Level $592$
Weight $2$
Character orbit 592.bj
Rep. character $\chi_{592}(269,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $296$
Newform subspaces $1$
Sturm bound $152$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.bj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 592 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(152\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(592, [\chi])\).

Total New Old
Modular forms 312 312 0
Cusp forms 296 296 0
Eisenstein series 16 16 0

Trace form

\( 296 q - 2 q^{2} - 2 q^{3} - 2 q^{5} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 16 q^{11} - 2 q^{12} - 2 q^{13} - 20 q^{14} - 4 q^{15} - 12 q^{16} - 4 q^{17} - 40 q^{18} - 2 q^{19} + 12 q^{20} - 14 q^{21} + 2 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(592, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.2.bj.a 592.bj 592.aj $296$ $4.727$ None 592.2.bj.a \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$