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Properties

Label 17.2.d
Level $17$
Weight $2$
Character orbit 17.d
Rep. character $\chi_{17}(2,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $4$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17.d (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(17, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} + 8 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} + 8 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 4 q^{14} - 8 q^{15} - 12 q^{16} - 12 q^{18} + 8 q^{19} + 4 q^{20} + 12 q^{22} + 4 q^{23} + 12 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} + 4 q^{28} - 4 q^{29} - 12 q^{31} + 4 q^{32} - 20 q^{34} + 8 q^{35} - 8 q^{40} - 4 q^{41} - 8 q^{42} - 8 q^{43} - 20 q^{44} + 12 q^{45} + 20 q^{46} + 12 q^{48} + 8 q^{49} + 20 q^{50} + 28 q^{51} + 16 q^{52} - 4 q^{53} - 8 q^{54} - 20 q^{56} - 24 q^{57} - 8 q^{60} - 12 q^{62} - 12 q^{63} - 4 q^{65} + 8 q^{66} + 16 q^{67} + 12 q^{68} - 32 q^{69} - 8 q^{70} + 20 q^{71} - 28 q^{73} + 20 q^{74} - 12 q^{75} + 8 q^{76} + 8 q^{77} - 8 q^{78} - 4 q^{79} + 4 q^{82} + 16 q^{83} + 32 q^{84} + 4 q^{85} + 8 q^{86} + 16 q^{87} + 12 q^{88} + 4 q^{90} - 28 q^{92} + 24 q^{93} - 24 q^{94} - 8 q^{95} - 20 q^{96} + 24 q^{97} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(17, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
17.2.d.a 17.d 17.d $4$ $0.136$ \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)