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Properties

Label 663.2.bt
Level $663$
Weight $2$
Character orbit 663.bt
Rep. character $\chi_{663}(98,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 663.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 663 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(663, [\chi])\).

Total New Old
Modular forms 352 352 0
Cusp forms 320 320 0
Eisenstein series 32 32 0

Trace form

\( 320 q - 2 q^{3} - 24 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} + O(q^{10}) \) \( 320 q - 2 q^{3} - 24 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} + 4 q^{10} - 8 q^{12} - 24 q^{13} - 24 q^{15} + 128 q^{16} + 8 q^{18} + 4 q^{19} - 24 q^{21} + 32 q^{22} + 24 q^{24} + 256 q^{25} + 16 q^{27} - 32 q^{28} - 12 q^{30} + 8 q^{33} - 12 q^{34} - 28 q^{37} - 14 q^{39} - 48 q^{40} - 24 q^{42} + 4 q^{43} - 18 q^{45} + 28 q^{46} - 96 q^{48} + 112 q^{49} - 44 q^{51} - 48 q^{52} - 132 q^{54} - 8 q^{55} + 44 q^{57} + 20 q^{58} - 28 q^{60} - 36 q^{61} - 68 q^{63} + 32 q^{67} - 12 q^{69} - 104 q^{70} - 128 q^{72} + 64 q^{73} - 90 q^{75} + 16 q^{76} + 10 q^{78} - 32 q^{79} - 12 q^{81} - 108 q^{82} + 120 q^{84} - 60 q^{85} - 108 q^{88} - 72 q^{90} - 12 q^{91} + 48 q^{93} + 48 q^{94} + 32 q^{96} + 72 q^{97} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(663, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
663.2.bt.a 663.bt 663.at $320$ $5.294$ None \(0\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{12}]$