Properties

Label 966.2.bd
Level $966$
Weight $2$
Character orbit 966.bd
Rep. character $\chi_{966}(59,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1280$
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.bd (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{66})\)
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 4000 1280 2720
Cusp forms 3680 1280 2400
Eisenstein series 320 0 320

Trace form

\( 1280q - 64q^{4} + 4q^{9} + O(q^{10}) \) \( 1280q - 64q^{4} + 4q^{9} + 16q^{15} + 64q^{16} - 44q^{18} + 120q^{21} - 16q^{22} - 12q^{24} + 56q^{25} + 32q^{30} - 24q^{33} + 8q^{36} - 44q^{37} - 20q^{39} + 4q^{42} + 136q^{43} + 12q^{45} + 12q^{46} + 92q^{49} + 4q^{51} - 36q^{54} - 56q^{57} - 28q^{58} + 8q^{60} + 72q^{61} - 134q^{63} + 128q^{64} + 24q^{67} - 72q^{70} - 44q^{72} - 72q^{73} + 48q^{75} - 16q^{78} - 72q^{79} + 40q^{81} + 48q^{82} - 10q^{84} - 32q^{85} + 222q^{87} - 8q^{88} - 8q^{91} - 16q^{93} + 72q^{94} - 12q^{96} - 68q^{99} + O(q^{100}) \)

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.bd.a \(1280\) \(7.714\) None \(0\) \(0\) \(0\) \(0\)

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

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