Properties

Label 17.4.d
Level 17
Weight 4
Character orbit d
Rep. character \(\chi_{17}(2,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 12
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
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: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(17, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut -\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut +\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut -\mathstrut 64q^{9} \) \(\mathstrut -\mathstrut 116q^{10} \) \(\mathstrut +\mathstrut 40q^{11} \) \(\mathstrut +\mathstrut 56q^{12} \) \(\mathstrut -\mathstrut 132q^{14} \) \(\mathstrut +\mathstrut 244q^{15} \) \(\mathstrut +\mathstrut 184q^{16} \) \(\mathstrut +\mathstrut 52q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 572q^{20} \) \(\mathstrut -\mathstrut 620q^{22} \) \(\mathstrut -\mathstrut 276q^{23} \) \(\mathstrut -\mathstrut 184q^{24} \) \(\mathstrut -\mathstrut 464q^{25} \) \(\mathstrut -\mathstrut 708q^{26} \) \(\mathstrut -\mathstrut 664q^{27} \) \(\mathstrut +\mathstrut 452q^{28} \) \(\mathstrut +\mathstrut 632q^{29} \) \(\mathstrut +\mathstrut 188q^{31} \) \(\mathstrut +\mathstrut 700q^{32} \) \(\mathstrut +\mathstrut 1400q^{33} \) \(\mathstrut +\mathstrut 764q^{34} \) \(\mathstrut -\mathstrut 632q^{35} \) \(\mathstrut +\mathstrut 524q^{36} \) \(\mathstrut +\mathstrut 940q^{37} \) \(\mathstrut -\mathstrut 1112q^{39} \) \(\mathstrut -\mathstrut 1864q^{40} \) \(\mathstrut +\mathstrut 176q^{41} \) \(\mathstrut +\mathstrut 48q^{42} \) \(\mathstrut -\mathstrut 1360q^{43} \) \(\mathstrut -\mathstrut 1364q^{44} \) \(\mathstrut -\mathstrut 32q^{45} \) \(\mathstrut +\mathstrut 452q^{46} \) \(\mathstrut -\mathstrut 540q^{48} \) \(\mathstrut +\mathstrut 1044q^{49} \) \(\mathstrut +\mathstrut 2856q^{50} \) \(\mathstrut +\mathstrut 340q^{51} \) \(\mathstrut +\mathstrut 792q^{52} \) \(\mathstrut -\mathstrut 360q^{53} \) \(\mathstrut -\mathstrut 244q^{54} \) \(\mathstrut -\mathstrut 1788q^{56} \) \(\mathstrut -\mathstrut 148q^{57} \) \(\mathstrut -\mathstrut 360q^{58} \) \(\mathstrut -\mathstrut 584q^{59} \) \(\mathstrut -\mathstrut 1792q^{60} \) \(\mathstrut -\mathstrut 1052q^{61} \) \(\mathstrut -\mathstrut 380q^{62} \) \(\mathstrut +\mathstrut 1752q^{63} \) \(\mathstrut +\mathstrut 404q^{65} \) \(\mathstrut +\mathstrut 1372q^{66} \) \(\mathstrut +\mathstrut 1080q^{67} \) \(\mathstrut +\mathstrut 2532q^{68} \) \(\mathstrut -\mathstrut 344q^{69} \) \(\mathstrut +\mathstrut 2072q^{70} \) \(\mathstrut +\mathstrut 28q^{71} \) \(\mathstrut +\mathstrut 824q^{73} \) \(\mathstrut -\mathstrut 2292q^{74} \) \(\mathstrut +\mathstrut 400q^{75} \) \(\mathstrut +\mathstrut 1328q^{76} \) \(\mathstrut -\mathstrut 1252q^{77} \) \(\mathstrut +\mathstrut 1128q^{78} \) \(\mathstrut -\mathstrut 196q^{79} \) \(\mathstrut -\mathstrut 904q^{80} \) \(\mathstrut -\mathstrut 1528q^{82} \) \(\mathstrut -\mathstrut 1008q^{83} \) \(\mathstrut -\mathstrut 4768q^{84} \) \(\mathstrut -\mathstrut 2824q^{85} \) \(\mathstrut -\mathstrut 1200q^{86} \) \(\mathstrut -\mathstrut 2516q^{87} \) \(\mathstrut -\mathstrut 56q^{88} \) \(\mathstrut -\mathstrut 860q^{90} \) \(\mathstrut +\mathstrut 2456q^{91} \) \(\mathstrut +\mathstrut 396q^{92} \) \(\mathstrut -\mathstrut 836q^{93} \) \(\mathstrut +\mathstrut 6360q^{94} \) \(\mathstrut +\mathstrut 2172q^{95} \) \(\mathstrut +\mathstrut 1668q^{96} \) \(\mathstrut -\mathstrut 904q^{97} \) \(\mathstrut +\mathstrut 3280q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(17, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.4.d.a \(12\) \(1.003\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(-4\) \(-20\) \(-4\) \(q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)