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Properties

Label 663.2.cp
Level $663$
Weight $2$
Character orbit 663.cp
Rep. character $\chi_{663}(28,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $672$
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.cp (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 221 \)
Character field: \(\Q(\zeta_{48})\)
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 1408 672 736
Cusp forms 1280 672 608
Eisenstein series 128 0 128

Trace form

\( 672 q + O(q^{10}) \) \( 672 q + 16 q^{13} - 64 q^{14} - 32 q^{17} - 80 q^{20} - 176 q^{22} - 32 q^{26} - 48 q^{28} + 32 q^{29} - 32 q^{31} + 160 q^{32} - 32 q^{33} + 64 q^{34} + 160 q^{38} + 16 q^{41} - 48 q^{42} - 32 q^{43} - 128 q^{44} - 16 q^{45} + 32 q^{46} - 32 q^{49} - 48 q^{53} - 32 q^{55} + 96 q^{58} - 128 q^{59} + 96 q^{61} - 192 q^{64} + 128 q^{67} - 64 q^{70} - 128 q^{71} + 128 q^{73} - 96 q^{74} + 128 q^{76} - 48 q^{78} - 128 q^{79} - 128 q^{80} - 112 q^{85} - 48 q^{87} + 16 q^{90} - 64 q^{91} + 128 q^{95} - 192 q^{96} - 48 q^{97} - 144 q^{98} + O(q^{100}) \)

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.cp.a 663.cp 221.ah $672$ $5.294$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$

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

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