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Properties

Label 522.2.x
Level $522$
Weight $2$
Character orbit 522.x
Rep. character $\chi_{522}(11,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $720$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 522.x (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 261 \)
Character field: \(\Q(\zeta_{84})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(522, [\chi])\).

Total New Old
Modular forms 2256 720 1536
Cusp forms 2064 720 1344
Eisenstein series 192 0 192

Trace form

\( 720 q + 24 q^{11} - 12 q^{14} - 20 q^{15} - 60 q^{16} + 84 q^{21} + 20 q^{24} + 60 q^{25} - 144 q^{27} - 12 q^{29} + 72 q^{30} + 84 q^{33} - 40 q^{36} + 40 q^{39} - 12 q^{41} - 104 q^{45} + 24 q^{46} - 24 q^{47}+ \cdots - 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(522, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
522.2.x.a 522.x 261.x $720$ $4.168$ None 522.2.x.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{84}]$

Decomposition of \(S_{2}^{\mathrm{old}}(522, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(522, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)