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Properties

Label 966.2.y
Level $966$
Weight $2$
Character orbit 966.y
Rep. character $\chi_{966}(25,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $640$
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.y (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
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 4000 640 3360
Cusp forms 3680 640 3040
Eisenstein series 320 0 320

Trace form

\( 640 q + 32 q^{4} + 8 q^{5} - 8 q^{7} + 32 q^{9} + O(q^{10}) \) \( 640 q + 32 q^{4} + 8 q^{5} - 8 q^{7} + 32 q^{9} - 8 q^{10} + 16 q^{11} - 8 q^{14} + 32 q^{16} - 16 q^{17} + 72 q^{20} + 16 q^{22} + 84 q^{23} + 104 q^{25} + 8 q^{26} - 72 q^{28} + 16 q^{29} - 8 q^{30} + 8 q^{31} - 8 q^{33} + 16 q^{34} + 20 q^{35} - 64 q^{36} + 44 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 16 q^{42} - 88 q^{43} + 16 q^{44} + 8 q^{45} - 4 q^{46} + 8 q^{47} + 48 q^{49} - 32 q^{50} + 52 q^{51} - 16 q^{53} - 16 q^{55} + 16 q^{56} - 72 q^{57} - 44 q^{58} + 96 q^{59} + 128 q^{61} - 48 q^{62} - 8 q^{63} - 64 q^{64} + 16 q^{65} - 16 q^{66} + 8 q^{67} - 16 q^{68} - 24 q^{69} + 96 q^{70} - 64 q^{71} + 40 q^{73} + 8 q^{74} + 16 q^{75} + 8 q^{77} - 88 q^{79} + 8 q^{80} + 32 q^{81} + 88 q^{82} + 144 q^{83} + 8 q^{85} + 24 q^{86} + 24 q^{87} - 8 q^{88} + 16 q^{89} + 16 q^{90} - 80 q^{91} + 8 q^{92} - 8 q^{93} + 16 q^{94} + 52 q^{95} + 64 q^{97} + 56 q^{98} + 56 q^{99} + O(q^{100}) \)

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.y.a 966.y 161.m $160$ $7.714$ None \(-8\) \(-8\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{33}]$
966.2.y.b 966.y 161.m $160$ $7.714$ None \(-8\) \(8\) \(6\) \(-10\) $\mathrm{SU}(2)[C_{33}]$
966.2.y.c 966.y 161.m $160$ $7.714$ None \(8\) \(-8\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{33}]$
966.2.y.d 966.y 161.m $160$ $7.714$ None \(8\) \(8\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{33}]$

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

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