Properties

Label 966.2.q
Level $966$
Weight $2$
Character orbit 966.q
Rep. character $\chi_{966}(85,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $240$
Newform subspaces $10$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.q (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 10 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 2000 240 1760
Cusp forms 1840 240 1600
Eisenstein series 160 0 160

Trace form

\( 240q - 24q^{4} - 24q^{9} + O(q^{10}) \) \( 240q - 24q^{4} - 24q^{9} - 16q^{11} - 32q^{13} - 16q^{15} - 24q^{16} + 56q^{17} + 56q^{19} - 4q^{21} + 72q^{22} + 56q^{23} + 24q^{25} + 72q^{26} + 56q^{29} - 16q^{30} + 40q^{31} - 16q^{33} - 16q^{34} - 16q^{35} - 24q^{36} + 12q^{37} - 32q^{38} + 72q^{39} + 56q^{41} - 4q^{42} - 4q^{43} - 16q^{44} - 24q^{46} + 112q^{47} - 24q^{49} - 16q^{50} + 28q^{51} - 32q^{52} + 40q^{53} + 112q^{55} + 28q^{57} - 40q^{58} - 64q^{59} - 16q^{60} - 48q^{61} - 32q^{62} - 24q^{64} - 48q^{65} - 32q^{66} + 24q^{67} - 32q^{68} - 16q^{69} - 8q^{70} - 80q^{71} - 8q^{73} - 32q^{75} - 32q^{76} - 8q^{78} - 40q^{79} - 24q^{81} - 32q^{82} + 56q^{83} - 4q^{84} + 24q^{85} - 32q^{86} - 32q^{87} - 16q^{88} + 24q^{89} + 72q^{91} - 32q^{92} - 56q^{93} - 16q^{94} - 8q^{95} - 8q^{97} - 16q^{99} + O(q^{100}) \)

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.q.a \(10\) \(7.714\) \(\Q(\zeta_{22})\) None \(-1\) \(-1\) \(-14\) \(1\) \(q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
966.2.q.b \(10\) \(7.714\) \(\Q(\zeta_{22})\) None \(-1\) \(-1\) \(2\) \(1\) \(q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
966.2.q.c \(10\) \(7.714\) \(\Q(\zeta_{22})\) None \(1\) \(-1\) \(0\) \(-1\) \(q-\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
966.2.q.d \(20\) \(7.714\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(2\) \(12\) \(-2\) \(q-\beta _{7}q^{2}-\beta _{19}q^{3}-\beta _{15}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
966.2.q.e \(20\) \(7.714\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(-2\) \(10\) \(-2\) \(q+\beta _{17}q^{2}+(-1-\beta _{4}-\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{3}+\cdots\)
966.2.q.f \(30\) \(7.714\) None \(3\) \(-3\) \(-10\) \(3\)
966.2.q.g \(30\) \(7.714\) None \(3\) \(3\) \(-10\) \(3\)
966.2.q.h \(30\) \(7.714\) None \(3\) \(3\) \(10\) \(-3\)
966.2.q.i \(40\) \(7.714\) None \(-4\) \(-4\) \(4\) \(-4\)
966.2.q.j \(40\) \(7.714\) None \(-4\) \(4\) \(-4\) \(4\)

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)