Properties

Label 663.2.bx
Level $663$
Weight $2$
Character orbit 663.bx
Rep. character $\chi_{663}(116,\cdot)$
Character field $\Q(\zeta_{16})$
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.bx (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 663 \)
Character field: \(\Q(\zeta_{16})\)
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

\( 640 q - 16 q^{3} - 32 q^{4} - 16 q^{9} + O(q^{10}) \) \( 640 q - 16 q^{3} - 32 q^{4} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 16 q^{13} - 32 q^{22} - 96 q^{25} - 16 q^{27} - 16 q^{30} - 48 q^{36} + 8 q^{39} - 32 q^{40} - 64 q^{42} - 32 q^{43} + 32 q^{48} - 16 q^{51} + 32 q^{52} - 64 q^{55} - 32 q^{61} + 96 q^{64} + 224 q^{66} - 224 q^{69} - 16 q^{75} - 112 q^{78} - 32 q^{79} - 16 q^{81} - 288 q^{82} + 80 q^{87} - 160 q^{88} - 96 q^{90} - 176 q^{91} - 160 q^{94} + O(q^{100}) \)

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.bx.a 663.bx 663.ax $640$ $5.294$ None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$