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Properties

Label 289.2.h
Level $289$
Weight $2$
Character orbit 289.h
Rep. character $\chi_{289}(4,\cdot)$
Character field $\Q(\zeta_{68})$
Dimension $768$
Newform subspaces $1$
Sturm bound $51$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 289.h (of order \(68\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{68})\)
Newform subspaces: \( 1 \)
Sturm bound: \(51\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(289, [\chi])\).

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

Trace form

\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + O(q^{10}) \) \( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + 34 q^{10} - 34 q^{11} - 34 q^{12} - 30 q^{13} - 34 q^{14} - 34 q^{15} - 82 q^{16} - 34 q^{17} - 42 q^{18} - 34 q^{19} - 34 q^{20} - 26 q^{21} - 34 q^{22} - 34 q^{23} - 204 q^{24} + 170 q^{25} - 34 q^{26} - 34 q^{27} - 34 q^{28} - 34 q^{29} - 14 q^{30} - 34 q^{31} - 34 q^{32} + 56 q^{33} - 34 q^{34} - 42 q^{35} - 34 q^{36} - 34 q^{37} + 144 q^{38} - 170 q^{39} - 34 q^{40} - 34 q^{41} - 34 q^{42} - 34 q^{43} - 34 q^{44} - 34 q^{45} + 102 q^{46} - 30 q^{47} - 34 q^{48} - 34 q^{49} - 62 q^{50} + 238 q^{51} - 50 q^{52} + 136 q^{54} - 14 q^{55} - 34 q^{56} - 34 q^{57} - 34 q^{58} - 34 q^{59} - 34 q^{60} - 34 q^{61} - 238 q^{62} - 34 q^{63} + 38 q^{64} - 34 q^{65} + 476 q^{66} + 82 q^{67} - 34 q^{68} - 62 q^{69} - 34 q^{70} - 34 q^{71} + 10 q^{72} - 34 q^{73} - 34 q^{74} + 102 q^{75} - 102 q^{76} - 374 q^{77} - 34 q^{78} + 68 q^{79} - 34 q^{80} + 30 q^{81} - 34 q^{82} + 102 q^{83} - 82 q^{84} - 204 q^{85} - 62 q^{86} - 34 q^{87} + 170 q^{88} - 22 q^{89} - 34 q^{90} - 34 q^{91} + 34 q^{92} - 34 q^{93} + 238 q^{94} - 34 q^{95} + 544 q^{96} - 34 q^{97} + 10 q^{98} - 34 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(289, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
289.2.h.a 289.h 289.h $768$ $2.308$ None \(-34\) \(-34\) \(-34\) \(-34\) $\mathrm{SU}(2)[C_{68}]$