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Properties

Label 666.2.bk
Level $666$
Weight $2$
Character orbit 666.bk
Rep. character $\chi_{666}(115,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $228$
Newform subspaces $1$
Sturm bound $228$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bk (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 333 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(228\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).

Total New Old
Modular forms 708 228 480
Cusp forms 660 228 432
Eisenstein series 48 0 48

Trace form

\( 228 q - 12 q^{3} + 6 q^{7} + 12 q^{9} + O(q^{10}) \) \( 228 q - 12 q^{3} + 6 q^{7} + 12 q^{9} - 12 q^{11} + 12 q^{12} + 6 q^{13} + 36 q^{21} + 36 q^{26} - 6 q^{27} - 6 q^{28} - 30 q^{33} + 18 q^{35} - 6 q^{37} + 36 q^{38} + 42 q^{39} - 120 q^{41} - 24 q^{42} + 72 q^{45} - 6 q^{49} + 6 q^{52} - 6 q^{53} - 54 q^{54} + 24 q^{57} - 6 q^{59} + 66 q^{63} + 114 q^{64} - 120 q^{67} + 12 q^{69} - 6 q^{71} - 24 q^{74} + 18 q^{75} - 24 q^{77} + 12 q^{78} + 6 q^{79} - 12 q^{81} + 18 q^{83} - 6 q^{87} - 60 q^{89} + 42 q^{90} - 42 q^{91} - 12 q^{92} - 36 q^{93} + 186 q^{95} - 48 q^{98} - 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
666.2.bk.a 666.bk 333.am $228$ $5.318$ None \(0\) \(-12\) \(0\) \(6\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)