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Properties

Label 414.3.o
Level $414$
Weight $3$
Character orbit 414.o
Rep. character $\chi_{414}(29,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $960$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 414.o (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(414, [\chi])\).

Total New Old
Modular forms 2960 960 2000
Cusp forms 2800 960 1840
Eisenstein series 160 0 160

Trace form

\( 960 q + 4 q^{3} - 96 q^{4} + 36 q^{5} + 16 q^{6} - 4 q^{9} - 8 q^{12} - 72 q^{14} + 300 q^{15} + 192 q^{16} - 160 q^{18} + 72 q^{20} - 158 q^{21} - 18 q^{23} + 16 q^{24} - 228 q^{25} + 310 q^{27} - 36 q^{29}+ \cdots - 816 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(414, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
414.3.o.a 414.o 207.n $960$ $11.281$ None 414.3.o.a \(0\) \(4\) \(36\) \(0\) $\mathrm{SU}(2)[C_{66}]$

Decomposition of \(S_{3}^{\mathrm{old}}(414, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)