Properties

Label 5.17.c
Level 5
Weight 17
Character orbit c
Rep. character \(\chi_{5}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 14
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 5.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(5, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

\( 14q - 2q^{2} + 7908q^{3} + 192880q^{5} + 4417368q^{6} - 386452q^{7} - 10493340q^{8} + O(q^{10}) \) \( 14q - 2q^{2} + 7908q^{3} + 192880q^{5} + 4417368q^{6} - 386452q^{7} - 10493340q^{8} + 398727830q^{10} - 539141632q^{11} + 1973309928q^{12} - 681358582q^{13} + 3514452060q^{15} - 22953579016q^{16} + 13124182498q^{17} - 11293583022q^{18} - 20186820060q^{20} + 133652286048q^{21} - 244784660624q^{22} + 236373052228q^{23} + 13144083650q^{25} + 223473840788q^{26} + 608106053880q^{27} - 1494176423768q^{28} + 2252131613760q^{30} - 1105223074952q^{31} - 2024535639992q^{32} - 6385551058704q^{33} + 6956678093980q^{35} + 12514339524924q^{36} - 9027827087002q^{37} - 7824802789560q^{38} + 31912538913900q^{40} + 39543901484288q^{41} - 70814500818384q^{42} - 63017457929452q^{43} + 126481294123110q^{45} + 44357914058008q^{46} - 2826187575452q^{47} - 405160526368272q^{48} + 461109216233650q^{50} + 208649050954008q^{51} - 389623094881012q^{52} - 275142037498442q^{53} + 330504874256560q^{55} + 865011118900080q^{56} - 644237427525840q^{57} - 991296507673440q^{58} + 1631207111049480q^{60} + 683634528395968q^{61} - 938995013191864q^{62} - 1361911146729372q^{63} + 517066464980110q^{65} - 196778043917184q^{66} - 181547742064252q^{67} - 917821658187868q^{68} + 1066699466039880q^{70} - 1337544011098792q^{71} + 2573199832214340q^{72} + 778038215296478q^{73} - 1442550824447700q^{75} - 233750796900240q^{76} + 1099376123524976q^{77} + 8472064951325256q^{78} - 14934736099860320q^{80} + 809940307363794q^{81} - 303814693723184q^{82} + 13357181209550188q^{83} - 16045734952112470q^{85} - 20034048539985352q^{86} + 17327533268211840q^{87} + 22952328705949920q^{88} - 21878453293909290q^{90} - 24534035720748632q^{91} + 40652972845631848q^{92} + 15958372062212256q^{93} - 22489885958711400q^{95} - 27488119051061472q^{96} - 3303551663290402q^{97} + 48233459501789102q^{98} + O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.17.c.a \(14\) \(8.116\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-2\) \(7908\) \(192880\) \(-386452\) \(q-\beta _{2}q^{2}+(565-3\beta _{1}-565\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)