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Properties

Label 663.2.bm
Level $663$
Weight $2$
Character orbit 663.bm
Rep. character $\chi_{663}(89,\cdot)$
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.bm (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

\( 320 q - 2 q^{3} - 24 q^{4} - 6 q^{6} - 4 q^{7} - 24 q^{9} + O(q^{10}) \) \( 320 q - 2 q^{3} - 24 q^{4} - 6 q^{6} - 4 q^{7} - 24 q^{9} + 20 q^{10} + 8 q^{12} - 24 q^{13} + 24 q^{15} + 128 q^{16} + 8 q^{18} - 4 q^{19} - 24 q^{21} - 40 q^{22} - 20 q^{24} - 256 q^{25} + 16 q^{27} - 72 q^{28} - 12 q^{30} - 32 q^{31} + 8 q^{33} - 52 q^{34} + 60 q^{37} + 18 q^{39} - 48 q^{40} + 24 q^{42} - 4 q^{43} - 6 q^{45} - 12 q^{46} + 132 q^{48} - 112 q^{49} + 44 q^{51} - 48 q^{52} + 56 q^{54} - 8 q^{55} + 12 q^{58} + 28 q^{60} - 36 q^{61} - 48 q^{63} + 32 q^{67} - 12 q^{69} + 104 q^{70} - 128 q^{72} - 18 q^{75} - 16 q^{76} + 18 q^{78} - 32 q^{79} - 12 q^{81} - 12 q^{82} + 120 q^{84} + 20 q^{85} - 60 q^{88} + 72 q^{90} - 52 q^{91} - 48 q^{93} - 48 q^{94} + 56 q^{97} + O(q^{100}) \)

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.bm.a 663.bm 663.am $320$ $5.294$ None \(0\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$