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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
966.2.s.a \(160\) \(7.714\) None \(-16\) \(0\) \(0\) \(0\)
966.2.s.b \(160\) \(7.714\) None \(16\) \(0\) \(0\) \(0\)

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

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