Properties

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

Related objects

Downloads

Learn more

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: \(\Q(i)\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{17}^{\mathrm{new}}(5, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5.17.c.a 5.c 5.c $14$ $8.116$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-2\) \(7908\) \(192880\) \(-386452\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+(565-3\beta _{1}-565\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)