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Properties

Label 558.2.z
Level $558$
Weight $2$
Character orbit 558.z
Rep. character $\chi_{558}(97,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $256$
Newform subspaces $2$
Sturm bound $192$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 558.z (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 279 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(558, [\chi])\).

Total New Old
Modular forms 800 256 544
Cusp forms 736 256 480
Eisenstein series 64 0 64

Trace form

\( 256 q + 4 q^{3} + 32 q^{4} - 4 q^{5} + 4 q^{7} + 4 q^{9} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 16 q^{15} + 32 q^{16} - 16 q^{17} + 8 q^{18} - 8 q^{19} - 4 q^{20} - 4 q^{21} - 24 q^{23} - 140 q^{25} + 112 q^{26}+ \cdots - 156 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(558, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
558.2.z.a 558.z 279.z $128$ $4.456$ None 558.2.z.a \(-16\) \(2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{15}]$
558.2.z.b 558.z 279.z $128$ $4.456$ None 558.2.z.b \(16\) \(2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(558, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(558, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 2}\)