Properties

Label 966.2.j
Level $966$
Weight $2$
Character orbit 966.j
Rep. character $\chi_{966}(137,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 400 128 272
Cusp forms 368 128 240
Eisenstein series 32 0 32

Trace form

\( 128q + 64q^{4} + 8q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 64q^{4} + 8q^{6} - 4q^{9} - 64q^{16} + 4q^{24} - 72q^{25} + 24q^{27} - 8q^{36} + 4q^{39} + 12q^{46} + 72q^{49} + 4q^{54} - 96q^{55} - 128q^{64} - 56q^{69} + 32q^{70} - 40q^{73} - 40q^{75} - 16q^{78} + 36q^{81} - 32q^{82} - 64q^{85} - 24q^{87} + 32q^{93} - 8q^{94} - 4q^{96} + O(q^{100}) \)

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.j.a \(128\) \(7.714\) None \(0\) \(0\) \(0\) \(0\)

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

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