Properties

Label 522.2.h
Level $522$
Weight $2$
Character orbit 522.h
Rep. character $\chi_{522}(115,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $60$
Newform subspaces $2$
Sturm bound $180$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 522.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 261 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(180\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 188 60 128
Cusp forms 172 60 112
Eisenstein series 16 0 16

Trace form

\( 60 q + 30 q^{4} - 4 q^{5} - 8 q^{6} + 20 q^{9} - 30 q^{16} + 4 q^{20} - 12 q^{23} - 4 q^{24} - 30 q^{25} - 12 q^{29} - 2 q^{30} - 30 q^{33} + 64 q^{35} + 16 q^{36} - 18 q^{38} - 12 q^{42} + 56 q^{45} - 42 q^{49}+ \cdots + 4 q^{96}+O(q^{100}) \) 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.h.a 522.h 261.i $4$ $4.168$ \(\Q(\zeta_{12})\) None 522.2.h.a \(0\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
522.2.h.b 522.h 261.i $56$ $4.168$ None 522.2.h.b \(0\) \(0\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{6}]$

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

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