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Properties

Label 663.2.by
Level $663$
Weight $2$
Character orbit 663.by
Rep. character $\chi_{663}(14,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $576$
Newform subspaces $2$
Sturm bound $168$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 663.by (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 51 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(663, [\chi])\).

Total New Old
Modular forms 704 576 128
Cusp forms 640 576 64
Eisenstein series 64 0 64

Trace form

\( 576 q + O(q^{10}) \) \( 576 q - 48 q^{12} - 48 q^{15} - 48 q^{21} - 48 q^{24} - 224 q^{34} - 64 q^{37} - 64 q^{40} + 48 q^{42} - 64 q^{43} - 32 q^{46} + 160 q^{48} + 32 q^{49} + 64 q^{51} + 32 q^{54} + 32 q^{55} - 112 q^{57} + 32 q^{61} - 144 q^{63} + 64 q^{64} + 16 q^{66} - 64 q^{70} - 128 q^{73} - 192 q^{75} - 128 q^{76} - 64 q^{79} - 112 q^{81} + 64 q^{85} - 192 q^{88} + 240 q^{90} + 192 q^{94} + 304 q^{96} + 144 q^{99} + O(q^{100}) \)

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.by.a 663.by 51.i $288$ $5.294$ None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$
663.2.by.b 663.by 51.i $288$ $5.294$ None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{16}]$

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

\( S_{2}^{\mathrm{old}}(663, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)