Properties

Label 17.3.e
Level 17
Weight 3
Character orbit e
Rep. character \(\chi_{17}(3,\cdot)\)
Character field \(\Q(\zeta_{16})\)
Dimension 16
Newforms 2
Sturm bound 4
Trace bound 2

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 17.e (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{16})\)
Newforms: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(17, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

Trace form

\(16q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 88q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 16q^{17} \) \(\mathstrut -\mathstrut 80q^{18} \) \(\mathstrut -\mathstrut 32q^{19} \) \(\mathstrut -\mathstrut 120q^{20} \) \(\mathstrut -\mathstrut 128q^{21} \) \(\mathstrut -\mathstrut 104q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 80q^{25} \) \(\mathstrut +\mathstrut 176q^{26} \) \(\mathstrut +\mathstrut 136q^{27} \) \(\mathstrut +\mathstrut 232q^{28} \) \(\mathstrut +\mathstrut 72q^{29} \) \(\mathstrut +\mathstrut 184q^{30} \) \(\mathstrut +\mathstrut 56q^{31} \) \(\mathstrut +\mathstrut 64q^{32} \) \(\mathstrut -\mathstrut 72q^{34} \) \(\mathstrut -\mathstrut 80q^{35} \) \(\mathstrut -\mathstrut 232q^{36} \) \(\mathstrut -\mathstrut 136q^{37} \) \(\mathstrut -\mathstrut 112q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 136q^{40} \) \(\mathstrut +\mathstrut 48q^{41} \) \(\mathstrut -\mathstrut 56q^{42} \) \(\mathstrut -\mathstrut 136q^{43} \) \(\mathstrut +\mathstrut 24q^{44} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 88q^{46} \) \(\mathstrut +\mathstrut 112q^{47} \) \(\mathstrut +\mathstrut 224q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 40q^{51} \) \(\mathstrut -\mathstrut 144q^{52} \) \(\mathstrut +\mathstrut 64q^{53} \) \(\mathstrut +\mathstrut 216q^{54} \) \(\mathstrut +\mathstrut 216q^{55} \) \(\mathstrut -\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 272q^{57} \) \(\mathstrut +\mathstrut 240q^{58} \) \(\mathstrut -\mathstrut 40q^{59} \) \(\mathstrut +\mathstrut 80q^{60} \) \(\mathstrut +\mathstrut 104q^{61} \) \(\mathstrut -\mathstrut 304q^{62} \) \(\mathstrut +\mathstrut 64q^{63} \) \(\mathstrut -\mathstrut 184q^{64} \) \(\mathstrut -\mathstrut 128q^{65} \) \(\mathstrut +\mathstrut 96q^{68} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 144q^{70} \) \(\mathstrut +\mathstrut 72q^{71} \) \(\mathstrut +\mathstrut 64q^{72} \) \(\mathstrut +\mathstrut 72q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 488q^{75} \) \(\mathstrut -\mathstrut 264q^{77} \) \(\mathstrut -\mathstrut 768q^{78} \) \(\mathstrut -\mathstrut 232q^{79} \) \(\mathstrut -\mathstrut 216q^{80} \) \(\mathstrut -\mathstrut 648q^{81} \) \(\mathstrut -\mathstrut 472q^{82} \) \(\mathstrut -\mathstrut 352q^{83} \) \(\mathstrut +\mathstrut 240q^{85} \) \(\mathstrut +\mathstrut 1120q^{86} \) \(\mathstrut +\mathstrut 520q^{87} \) \(\mathstrut +\mathstrut 440q^{88} \) \(\mathstrut +\mathstrut 448q^{89} \) \(\mathstrut +\mathstrut 704q^{90} \) \(\mathstrut +\mathstrut 296q^{91} \) \(\mathstrut +\mathstrut 360q^{92} \) \(\mathstrut +\mathstrut 216q^{93} \) \(\mathstrut +\mathstrut 24q^{94} \) \(\mathstrut +\mathstrut 120q^{95} \) \(\mathstrut +\mathstrut 272q^{96} \) \(\mathstrut -\mathstrut 296q^{97} \) \(\mathstrut -\mathstrut 104q^{98} \) \(\mathstrut -\mathstrut 88q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(17, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.3.e.a \(8\) \(0.463\) \(\Q(\zeta_{16})\) None \(-8\) \(-8\) \(16\) \(8\) \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
17.3.e.b \(8\) \(0.463\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-24\) \(-16\) \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)