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Properties

Label 663.2.bh
Level $663$
Weight $2$
Character orbit 663.bh
Rep. character $\chi_{663}(25,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $176$
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.bh (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 221 \)
Character field: \(\Q(\zeta_{8})\)
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 352 176 176
Cusp forms 320 176 144
Eisenstein series 32 0 32

Trace form

\( 176 q + O(q^{10}) \) \( 176 q - 16 q^{10} - 48 q^{14} - 224 q^{16} + 16 q^{17} + 64 q^{22} - 16 q^{23} - 64 q^{25} - 8 q^{26} + 64 q^{29} - 16 q^{39} + 48 q^{42} + 32 q^{43} - 32 q^{52} + 112 q^{53} - 80 q^{56} + 48 q^{61} - 80 q^{62} - 96 q^{65} - 32 q^{66} - 64 q^{68} - 80 q^{69} + 160 q^{74} + 16 q^{77} - 8 q^{78} + 48 q^{79} - 96 q^{82} + 48 q^{87} + 64 q^{88} + 16 q^{90} - 16 q^{91} - 64 q^{94} + 64 q^{95} + O(q^{100}) \)

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.bh.a 663.bh 221.p $176$ $5.294$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

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