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Properties

Label 968.2.q
Level $968$
Weight $2$
Character orbit 968.q
Rep. character $\chi_{968}(89,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $330$
Newform subspaces $2$
Sturm bound $264$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 968.q (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(264\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(968, [\chi])\).

Total New Old
Modular forms 1360 330 1030
Cusp forms 1280 330 950
Eisenstein series 80 0 80

Trace form

\( 330 q + 2 q^{3} + 4 q^{7} + 324 q^{9} + O(q^{10}) \) \( 330 q + 2 q^{3} + 4 q^{7} + 324 q^{9} + 3 q^{11} + 2 q^{13} + 4 q^{15} + 2 q^{17} + 4 q^{19} + 12 q^{21} - 12 q^{23} - 37 q^{25} + 8 q^{27} + 10 q^{29} + 12 q^{31} - 2 q^{33} - 20 q^{35} + 8 q^{37} - 16 q^{39} - 10 q^{41} + 28 q^{45} - 4 q^{47} - 53 q^{49} + 35 q^{51} + 18 q^{53} + 132 q^{55} + 49 q^{57} + 6 q^{59} + 2 q^{61} + 32 q^{63} + 20 q^{65} - 18 q^{67} - 8 q^{69} - 44 q^{71} - 18 q^{73} + 34 q^{75} + 128 q^{77} + 78 q^{79} + 330 q^{81} - 8 q^{83} - 24 q^{85} - 40 q^{87} - 46 q^{89} + 24 q^{91} - 28 q^{93} + 24 q^{95} - 18 q^{97} + 9 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(968, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
968.2.q.a 968.q 121.e $160$ $7.730$ None 968.2.q.a \(0\) \(-8\) \(3\) \(2\) $\mathrm{SU}(2)[C_{11}]$
968.2.q.b 968.q 121.e $170$ $7.730$ None 968.2.q.b \(0\) \(10\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(968, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(968, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 2}\)