↑

Properties

Label 867.2.k
Level $867$
Weight $2$
Character orbit 867.k
Rep. character $\chi_{867}(52,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $832$
Newform subspaces $2$
Sturm bound $204$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 867 = 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 867.k (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{17})\)
Newform subspaces: \( 2 \)
Sturm bound: \(204\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(867, [\chi])\).

Total New Old
Modular forms 1664 832 832
Cusp forms 1600 832 768
Eisenstein series 64 0 64

Trace form

\( 832 q - 2 q^{2} - 58 q^{4} + 56 q^{5} - 4 q^{6} - 4 q^{7} - 6 q^{8} - 52 q^{9} + O(q^{10}) \) \( 832 q - 2 q^{2} - 58 q^{4} + 56 q^{5} - 4 q^{6} - 4 q^{7} - 6 q^{8} - 52 q^{9} + 26 q^{10} - 8 q^{11} - 16 q^{13} - 24 q^{14} - 4 q^{15} + 118 q^{16} - 18 q^{17} - 2 q^{18} - 20 q^{19} - 52 q^{20} - 4 q^{21} - 28 q^{22} - 24 q^{23} - 24 q^{24} + 52 q^{25} - 48 q^{26} - 64 q^{28} - 36 q^{29} - 28 q^{30} - 32 q^{31} - 54 q^{32} - 8 q^{33} - 50 q^{34} - 28 q^{35} - 58 q^{36} - 32 q^{37} + 60 q^{38} - 8 q^{39} - 68 q^{40} - 36 q^{41} - 24 q^{42} - 24 q^{43} + 40 q^{44} - 12 q^{45} + 10 q^{47} - 32 q^{48} - 96 q^{49} - 58 q^{50} - 14 q^{51} + 74 q^{52} - 18 q^{53} + 30 q^{54} - 60 q^{55} - 120 q^{56} - 16 q^{57} + 114 q^{58} - 60 q^{59} - 12 q^{60} - 80 q^{61} - 80 q^{62} + 30 q^{63} - 162 q^{64} - 80 q^{65} - 32 q^{66} + 8 q^{67} - 126 q^{68} - 40 q^{69} - 124 q^{70} + 184 q^{71} - 6 q^{72} - 68 q^{73} + 242 q^{74} + 104 q^{75} - 70 q^{76} + 236 q^{77} - 36 q^{78} + 94 q^{79} + 112 q^{80} - 52 q^{81} - 136 q^{82} + 76 q^{83} - 52 q^{84} + 272 q^{85} - 100 q^{86} - 28 q^{87} + 164 q^{88} - 84 q^{89} - 8 q^{90} + 20 q^{91} + 204 q^{92} - 36 q^{93} + 294 q^{94} - 96 q^{95} - 4 q^{96} - 68 q^{97} - 142 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(867, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
867.2.k.a 867.k 289.f $416$ $6.923$ None \(-3\) \(-26\) \(26\) \(-4\) $\mathrm{SU}(2)[C_{17}]$
867.2.k.b 867.k 289.f $416$ $6.923$ None \(1\) \(26\) \(30\) \(0\) $\mathrm{SU}(2)[C_{17}]$

Decomposition of \(S_{2}^{\mathrm{old}}(867, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(867, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)