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Properties

Label 966.2.s
Level $966$
Weight $2$
Character orbit 966.s
Rep. character $\chi_{966}(97,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $320$
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.s (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{22})\)
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 2000 320 1680
Cusp forms 1840 320 1520
Eisenstein series 160 0 160

Trace form

\( 320 q - 32 q^{4} + 32 q^{9} + O(q^{10}) \) \( 320 q - 32 q^{4} + 32 q^{9} - 32 q^{16} - 88 q^{23} + 48 q^{25} + 44 q^{28} - 32 q^{29} - 28 q^{35} + 32 q^{36} + 44 q^{37} + 44 q^{43} + 16 q^{46} - 32 q^{50} + 44 q^{51} + 44 q^{57} + 80 q^{58} - 32 q^{64} - 72 q^{70} + 64 q^{71} - 48 q^{77} + 8 q^{78} + 176 q^{79} - 32 q^{81} + 8 q^{85} - 8 q^{93} - 80 q^{95} + 88 q^{98} - 88 q^{99} + O(q^{100}) \)

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.s.a 966.s 161.k $160$ $7.714$ None \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
966.2.s.b 966.s 161.k $160$ $7.714$ None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

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

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