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Properties

Label 213.2.n
Level $213$
Weight $2$
Character orbit 213.n
Rep. character $\chi_{213}(11,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $528$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 213 = 3 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 213.n (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 213 \)
Character field: \(\Q(\zeta_{70})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(213, [\chi])\).

Total New Old
Modular forms 624 624 0
Cusp forms 528 528 0
Eisenstein series 96 96 0

Trace form

\( 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(213, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
213.2.n.a 213.n 213.n $528$ $1.701$ None 213.2.n.a \(0\) \(-20\) \(0\) \(-46\) $\mathrm{SU}(2)[C_{70}]$