Properties

Label 966.2.bf
Level $966$
Weight $2$
Character orbit 966.bf
Rep. character $\chi_{966}(11,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1280$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.bf (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

\( 1280q - 64q^{4} - 8q^{6} + 4q^{9} + O(q^{10}) \) \( 1280q - 64q^{4} - 8q^{6} + 4q^{9} + 64q^{16} + 44q^{18} - 132q^{21} - 4q^{24} + 72q^{25} + 108q^{27} + 44q^{30} + 8q^{36} + 44q^{37} - 4q^{39} - 88q^{43} - 12q^{46} + 60q^{49} - 48q^{54} + 96q^{55} + 44q^{58} - 176q^{61} - 110q^{63} + 128q^{64} + 56q^{69} - 120q^{70} + 44q^{72} + 40q^{73} - 268q^{75} + 16q^{78} + 88q^{79} + 8q^{81} - 56q^{82} - 22q^{84} + 64q^{85} - 42q^{87} - 32q^{93} + 8q^{94} + 4q^{96} + 132q^{99} + O(q^{100}) \)

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

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

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