Properties

Label 17.2.d
Level 17
Weight 2
Character orbit d
Rep. character \(\chi_{17}(2,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 4
Newforms 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: \(\Q(\zeta_{8})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(17, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.2.d.a \(4\) \(0.136\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(-4\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)