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Properties

Label 663.2.cg
Level $663$
Weight $2$
Character orbit 663.cg
Rep. character $\chi_{663}(94,\cdot)$
Character field $\Q(\zeta_{24})$
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.cg (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 221 \)
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 704 320 384
Cusp forms 640 320 320
Eisenstein series 64 0 64

Trace form

\( 320 q + O(q^{10}) \) \( 320 q + 96 q^{14} + 112 q^{16} + 16 q^{17} + 16 q^{20} - 40 q^{22} + 8 q^{23} + 48 q^{25} - 16 q^{26} + 24 q^{28} + 8 q^{29} - 32 q^{31} + 120 q^{32} - 8 q^{33} - 64 q^{34} - 16 q^{39} - 8 q^{41} + 24 q^{42} - 16 q^{43} - 8 q^{45} + 16 q^{46} - 32 q^{52} + 16 q^{53} + 40 q^{56} - 64 q^{58} + 32 q^{59} - 48 q^{61} - 40 q^{62} - 120 q^{65} + 32 q^{66} - 32 q^{67} + 32 q^{68} + 72 q^{69} + 64 q^{70} + 128 q^{71} - 112 q^{73} - 32 q^{74} - 32 q^{76} + 32 q^{77} - 8 q^{78} - 96 q^{79} - 64 q^{80} + 40 q^{82} - 40 q^{85} - 256 q^{86} + 24 q^{87} - 64 q^{88} - 32 q^{91} + 32 q^{94} - 32 q^{95} - 192 q^{96} - 24 q^{97} + O(q^{100}) \)

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.cg.a 663.cg 221.ae $320$ $5.294$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{24}]$

Decomposition of \(S_{2}^{\mathrm{old}}(663, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(663, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(221, [\chi])\)\(^{\oplus 2}\)