Properties

Label 966.2.t
Level $966$
Weight $2$
Character orbit 966.t
Rep. character $\chi_{966}(41,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $640$
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.t (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{22})\)
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 2000 640 1360
Cusp forms 1840 640 1200
Eisenstein series 160 0 160

Trace form

\( 640q + 64q^{4} + 8q^{9} + O(q^{10}) \) \( 640q + 64q^{4} + 8q^{9} + 8q^{15} - 64q^{16} + 20q^{18} + 54q^{21} - 8q^{22} - 56q^{25} - 44q^{30} - 8q^{36} + 20q^{37} - 16q^{39} - 4q^{42} - 28q^{43} + 24q^{46} - 68q^{49} - 40q^{51} + 32q^{57} - 80q^{58} - 8q^{60} + 86q^{63} + 64q^{64} + 24q^{67} + 72q^{70} - 64q^{72} - 8q^{78} - 144q^{79} + 20q^{81} + 34q^{84} + 32q^{85} + 8q^{88} - 40q^{91} + 16q^{93} + 68q^{99} + O(q^{100}) \)

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.t.a \(640\) \(7.714\) None \(0\) \(0\) \(0\) \(0\)

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

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