Properties

Label 966.2.h
Level $966$
Weight $2$
Character orbit 966.h
Rep. character $\chi_{966}(827,\cdot)$
Character field $\Q$
Dimension $48$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 200 48 152
Cusp forms 184 48 136
Eisenstein series 16 0 16

Trace form

\( 48q + 8q^{3} - 48q^{4} - 8q^{9} + O(q^{10}) \) \( 48q + 8q^{3} - 48q^{4} - 8q^{9} - 8q^{12} + 16q^{13} + 48q^{16} + 8q^{18} - 24q^{25} + 32q^{27} - 32q^{31} + 8q^{36} - 16q^{39} - 8q^{46} + 8q^{48} - 48q^{49} - 16q^{52} - 24q^{54} + 32q^{55} + 8q^{58} - 48q^{64} - 48q^{69} - 8q^{70} - 8q^{72} - 64q^{73} + 96q^{75} + 24q^{78} - 16q^{81} - 16q^{82} - 32q^{85} + 40q^{87} + 32q^{93} + 16q^{94} + O(q^{100}) \)

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.h.a \(24\) \(7.714\) None \(0\) \(4\) \(-4\) \(0\)
966.2.h.b \(24\) \(7.714\) None \(0\) \(4\) \(4\) \(0\)

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

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