Properties

Label 966.2.be
Level $966$
Weight $2$
Character orbit 966.be
Rep. character $\chi_{966}(19,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $640$
Newform subspaces $2$
Sturm bound $384$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.be (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 4000 640 3360
Cusp forms 3680 640 3040
Eisenstein series 320 0 320

Trace form

\( 640q + 32q^{4} - 32q^{9} + O(q^{10}) \) \( 640q + 32q^{4} - 32q^{9} + 32q^{16} + 76q^{23} - 24q^{25} + 24q^{26} + 88q^{28} - 16q^{29} - 24q^{31} + 52q^{35} + 64q^{36} - 44q^{37} + 88q^{43} - 4q^{46} - 24q^{47} - 48q^{49} + 32q^{50} - 44q^{51} + 88q^{57} + 28q^{58} + 24q^{59} - 64q^{64} - 64q^{71} + 72q^{73} - 48q^{75} - 24q^{77} - 32q^{78} + 88q^{79} + 32q^{81} + 48q^{82} - 8q^{85} + 72q^{87} + 24q^{92} + 8q^{93} + 92q^{95} - 88q^{98} + 88q^{99} + O(q^{100}) \)

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.be.a \(320\) \(7.714\) None \(-16\) \(0\) \(0\) \(0\)
966.2.be.b \(320\) \(7.714\) None \(16\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)