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Properties

Label 289.2.f
Level $289$
Weight $2$
Character orbit 289.f
Rep. character $\chi_{289}(18,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $384$
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.f (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{17})\)
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 416 416 0
Cusp forms 384 384 0
Eisenstein series 32 32 0

Trace form

\( 384 q - 13 q^{2} - 13 q^{3} - 33 q^{4} - 43 q^{5} - 5 q^{6} - 13 q^{7} - 5 q^{8} - 25 q^{9} + O(q^{10}) \) \( 384 q - 13 q^{2} - 13 q^{3} - 33 q^{4} - 43 q^{5} - 5 q^{6} - 13 q^{7} - 5 q^{8} - 25 q^{9} - 35 q^{10} - 5 q^{11} + 11 q^{12} - 3 q^{13} - 74 q^{14} + 5 q^{15} - 145 q^{16} - q^{17} + 15 q^{18} + 5 q^{19} + 23 q^{20} - 40 q^{21} + 19 q^{22} + 3 q^{23} - 42 q^{24} - 113 q^{25} + 19 q^{26} - 28 q^{27} + 43 q^{28} + 7 q^{29} + 45 q^{30} + 11 q^{31} + 41 q^{32} - 26 q^{33} + 35 q^{34} + 35 q^{35} + 37 q^{36} + 23 q^{37} - 152 q^{38} - 29 q^{39} + 62 q^{40} + 31 q^{41} + 65 q^{42} + 17 q^{43} - q^{44} - 98 q^{45} - 9 q^{46} + 12 q^{47} - 114 q^{48} + 5 q^{49} + 61 q^{50} - 85 q^{51} - 116 q^{52} + 8 q^{53} - 356 q^{54} + 45 q^{55} + 91 q^{56} + 63 q^{57} - 40 q^{58} + 49 q^{59} + 133 q^{60} + 55 q^{61} - 19 q^{62} + 14 q^{63} + 67 q^{64} + 46 q^{65} - 144 q^{66} - 82 q^{67} + 103 q^{68} - 54 q^{69} + 103 q^{70} - 77 q^{71} + 114 q^{72} + 63 q^{73} - 92 q^{74} - 46 q^{75} - 71 q^{76} - 105 q^{77} + 151 q^{78} - 68 q^{79} - 37 q^{80} - 73 q^{81} + 103 q^{82} - 5 q^{83} + 183 q^{84} - 168 q^{85} + 105 q^{86} + 91 q^{87} - 75 q^{88} + 57 q^{89} + 223 q^{90} + 35 q^{91} - 15 q^{92} + 95 q^{93} - 331 q^{94} + 95 q^{95} - 122 q^{96} + 79 q^{97} - 63 q^{98} + 139 q^{99} + O(q^{100}) \)

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.f.a 289.f 289.f $384$ $2.308$ None \(-13\) \(-13\) \(-43\) \(-13\) $\mathrm{SU}(2)[C_{17}]$