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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(966, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
966.2.l.a 966.l 21.g $4$ $7.714$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\cdots\)
966.2.l.b 966.l 21.g $4$ $7.714$ \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2})q^{3}+\cdots\)
966.2.l.c 966.l 21.g $56$ $7.714$ None \(0\) \(-6\) \(0\) \(20\) $\mathrm{SU}(2)[C_{6}]$
966.2.l.d 966.l 21.g $56$ $7.714$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$

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

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