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Properties

Label 959.2.o
Level $959$
Weight $2$
Character orbit 959.o
Rep. character $\chi_{959}(50,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $1120$
Newform subspaces $2$
Sturm bound $184$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 959 = 7 \cdot 137 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 959.o (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 137 \)
Character field: \(\Q(\zeta_{17})\)
Newform subspaces: \( 2 \)
Sturm bound: \(184\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(959, [\chi])\).

Total New Old
Modular forms 1504 1120 384
Cusp forms 1440 1120 320
Eisenstein series 64 0 64

Trace form

\( 1120 q - 6 q^{2} - 8 q^{3} - 14 q^{4} - 12 q^{5} - 12 q^{6} - 2 q^{7} - 18 q^{8} - 90 q^{9} + O(q^{10}) \) \( 1120 q - 6 q^{2} - 8 q^{3} - 14 q^{4} - 12 q^{5} - 12 q^{6} - 2 q^{7} - 18 q^{8} - 90 q^{9} - 36 q^{10} - 16 q^{11} + 58 q^{12} - 16 q^{13} - 6 q^{14} - 36 q^{15} - 62 q^{16} + 108 q^{17} - 38 q^{18} - 28 q^{19} - 36 q^{20} - 44 q^{22} + 10 q^{23} - 36 q^{24} - 110 q^{25} - 20 q^{26} + 148 q^{27} - 14 q^{28} - 36 q^{29} - 52 q^{30} + 42 q^{31} - 62 q^{32} - 64 q^{33} - 88 q^{34} - 190 q^{36} + 4 q^{37} + 190 q^{38} - 68 q^{39} - 160 q^{40} - 76 q^{41} - 20 q^{42} - 56 q^{43} + 35 q^{44} + 228 q^{45} + 48 q^{46} - 36 q^{47} - 100 q^{48} - 70 q^{49} - 98 q^{50} - 72 q^{51} - 60 q^{52} + 264 q^{53} + 30 q^{54} - 72 q^{55} - 30 q^{56} + 128 q^{57} + 178 q^{58} + 46 q^{60} - 88 q^{61} - 8 q^{62} - 18 q^{63} + 204 q^{64} - 116 q^{65} - 148 q^{66} + 8 q^{67} - 144 q^{68} - 160 q^{69} - 14 q^{71} - 16 q^{72} - 128 q^{73} + 22 q^{74} + 184 q^{75} - 108 q^{76} - 24 q^{77} - 124 q^{78} - 32 q^{79} - 112 q^{80} - 286 q^{81} + 56 q^{82} - 84 q^{83} - 128 q^{85} - 12 q^{86} + 68 q^{87} - 95 q^{88} - 124 q^{89} - 212 q^{90} - 76 q^{92} - 120 q^{93} + 76 q^{94} - 56 q^{95} - 176 q^{96} + 354 q^{97} - 6 q^{98} + 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(959, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
959.2.o.a 959.o 137.e $544$ $7.658$ None 959.2.o.a \(0\) \(-4\) \(-6\) \(34\) $\mathrm{SU}(2)[C_{17}]$
959.2.o.b 959.o 137.e $576$ $7.658$ None 959.2.o.b \(-6\) \(-4\) \(-6\) \(-36\) $\mathrm{SU}(2)[C_{17}]$

Decomposition of \(S_{2}^{\mathrm{old}}(959, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(959, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(137, [\chi])\)\(^{\oplus 2}\)