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Properties

Label 966.2.k
Level $966$
Weight $2$
Character orbit 966.k
Rep. character $\chi_{966}(229,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
Sturm bound $384$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(966, [\chi])\).

Total New Old
Modular forms 400 64 336
Cusp forms 368 64 304
Eisenstein series 32 0 32

Trace form

\( 64 q - 32 q^{4} + 32 q^{9} + O(q^{10}) \) \( 64 q - 32 q^{4} + 32 q^{9} - 32 q^{16} + 12 q^{23} - 64 q^{25} - 24 q^{26} + 16 q^{29} + 24 q^{31} - 8 q^{35} - 64 q^{36} + 4 q^{46} + 24 q^{47} + 48 q^{49} - 32 q^{50} + 16 q^{58} - 24 q^{59} + 64 q^{64} + 88 q^{70} + 64 q^{71} - 72 q^{73} + 48 q^{75} + 24 q^{77} + 32 q^{78} - 32 q^{81} - 48 q^{82} - 80 q^{85} - 72 q^{87} - 24 q^{92} - 8 q^{93} + 40 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(966, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
966.2.k.a 966.k 161.g $32$ $7.714$ None \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
966.2.k.b 966.k 161.g $32$ $7.714$ None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(966, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)