Properties

Label 966.2.r
Level $966$
Weight $2$
Character orbit 966.r
Rep. character $\chi_{966}(113,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $480$
Newform subspaces $2$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.r (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(5\)
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 480 1520
Cusp forms 1840 480 1360
Eisenstein series 160 0 160

Trace form

\( 480q - 8q^{3} + 48q^{4} + 8q^{9} + O(q^{10}) \) \( 480q - 8q^{3} + 48q^{4} + 8q^{9} + 8q^{12} - 16q^{13} + 44q^{15} - 48q^{16} + 36q^{18} + 24q^{25} - 32q^{27} + 44q^{30} + 32q^{31} + 44q^{33} - 8q^{36} + 44q^{37} + 16q^{39} + 44q^{43} + 8q^{46} - 8q^{48} + 48q^{49} + 16q^{52} + 24q^{54} - 32q^{55} - 132q^{57} - 8q^{58} - 44q^{60} + 48q^{64} - 176q^{66} - 88q^{67} - 172q^{69} + 8q^{70} + 8q^{72} - 24q^{73} - 52q^{75} - 156q^{78} - 116q^{81} + 16q^{82} - 56q^{85} - 40q^{87} - 32q^{93} - 16q^{94} + 264q^{97} + O(q^{100}) \)

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.r.a \(240\) \(7.714\) None \(0\) \(-4\) \(-4\) \(0\)
966.2.r.b \(240\) \(7.714\) None \(0\) \(-4\) \(4\) \(0\)

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)