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

Related objects

Downloads

Learn more about

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

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

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 \(-4\) \(-4\) \(0\) \(-4\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)