Properties

Label 966.2.l
Level $966$
Weight $2$
Character orbit 966.l
Rep. character $\chi_{966}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Newform subspaces $4$
Sturm bound $384$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(384\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 400 120 280
Cusp forms 368 120 248
Eisenstein series 32 0 32

Trace form

\( 120q + 60q^{4} + 20q^{7} + 8q^{9} + O(q^{10}) \) \( 120q + 60q^{4} + 20q^{7} + 8q^{9} + 12q^{10} - 40q^{15} - 60q^{16} - 24q^{19} + 12q^{21} - 8q^{22} - 64q^{25} + 4q^{28} + 12q^{30} + 12q^{31} + 60q^{33} + 16q^{36} - 8q^{37} + 20q^{39} + 12q^{40} + 8q^{42} + 16q^{43} - 12q^{45} - 4q^{49} - 28q^{51} - 24q^{52} + 56q^{57} - 28q^{58} - 20q^{60} - 72q^{61} - 24q^{63} - 120q^{64} - 16q^{67} - 52q^{70} + 24q^{73} - 48q^{75} + 64q^{78} - 20q^{79} + 40q^{81} - 12q^{84} + 80q^{85} + 12q^{87} - 4q^{88} + 32q^{91} + 16q^{93} - 24q^{94} - 64q^{99} + O(q^{100}) \)

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.l.a \(4\) \(7.714\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\cdots\)
966.2.l.b \(4\) \(7.714\) \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(-10\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2})q^{3}+\cdots\)
966.2.l.c \(56\) \(7.714\) None \(0\) \(-6\) \(0\) \(20\)
966.2.l.d \(56\) \(7.714\) None \(0\) \(0\) \(0\) \(8\)

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

\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)