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Properties

Label 668.2.e
Level $668$
Weight $2$
Character orbit 668.e
Rep. character $\chi_{668}(9,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $1148$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(668, [\chi])\).

Total New Old
Modular forms 7134 1148 5986
Cusp forms 6642 1148 5494
Eisenstein series 492 0 492

Trace form

\( 1148 q - 2 q^{5} - 14 q^{9} + O(q^{10}) \) \( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(668, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
668.2.e.a 668.e 167.c $1148$ $5.334$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{83}]$

Decomposition of \(S_{2}^{\mathrm{old}}(668, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(668, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(334, [\chi])\)\(^{\oplus 2}\)