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Properties

Label 663.2.cf
Level $663$
Weight $2$
Character orbit 663.cf
Rep. character $\chi_{663}(110,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $640$
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.cf (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 663 \)
Character field: \(\Q(\zeta_{24})\)
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 704 704 0
Cusp forms 640 640 0
Eisenstein series 64 64 0

Trace form

\( 640 q - 4 q^{3} - 304 q^{4} - 16 q^{7} - 4 q^{9} + O(q^{10}) \) \( 640 q - 4 q^{3} - 304 q^{4} - 16 q^{7} - 4 q^{9} - 88 q^{10} + 16 q^{12} - 36 q^{15} - 288 q^{16} - 24 q^{19} + 32 q^{21} - 8 q^{22} - 8 q^{24} + 32 q^{25} - 64 q^{27} + 8 q^{28} + 32 q^{30} - 32 q^{31} - 48 q^{33} + 32 q^{34} - 20 q^{36} - 112 q^{37} - 12 q^{39} + 32 q^{40} + 44 q^{42} - 40 q^{43} + 56 q^{45} + 32 q^{46} - 68 q^{48} - 40 q^{49} - 64 q^{51} + 32 q^{52} + 104 q^{54} - 4 q^{57} - 48 q^{58} - 8 q^{61} + 16 q^{63} + 480 q^{64} - 120 q^{66} - 64 q^{67} - 24 q^{69} - 208 q^{72} - 96 q^{73} - 56 q^{75} - 72 q^{76} + 164 q^{78} - 64 q^{79} - 48 q^{81} + 8 q^{82} - 32 q^{84} - 8 q^{85} + 68 q^{87} - 104 q^{88} + 16 q^{90} + 96 q^{91} - 28 q^{93} - 56 q^{94} + 40 q^{96} + 64 q^{97} + 52 q^{99} + O(q^{100}) \)

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.cf.a 663.cf 663.bf $640$ $5.294$ None \(0\) \(-4\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{24}]$