Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 5x^{11} - 11x^{10} - 76x^{9} + 22x^{8} + 363x^{7} - 22x^{6} - 754x^{5} + 108x^{4} + 648x^{3} - 158x^{2} - 162x + 39\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $\phantom{-}\frac{217}{927}e^{11} + \frac{1387}{927}e^{10} - \frac{269}{309}e^{9} - \frac{18619}{927}e^{8} - \frac{16375}{927}e^{7} + \frac{68554}{927}e^{6} + \frac{72298}{927}e^{5} - \frac{100811}{927}e^{4} - \frac{86725}{927}e^{3} + \frac{54292}{927}e^{2} + \frac{8345}{309}e - \frac{1850}{309}$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $\phantom{-}\frac{1841}{927}e^{11} + \frac{11498}{927}e^{10} - \frac{2023}{309}e^{9} - \frac{147824}{927}e^{8} - \frac{141824}{927}e^{7} + \frac{495482}{927}e^{6} + \frac{570695}{927}e^{5} - \frac{684550}{927}e^{4} - \frac{646682}{927}e^{3} + \frac{386237}{927}e^{2} + \frac{63352}{309}e - \frac{19144}{309}$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $\phantom{-}\frac{3364}{927}e^{11} + \frac{20878}{927}e^{10} - \frac{3854}{309}e^{9} - \frac{268897}{927}e^{8} - \frac{254098}{927}e^{7} + \frac{905407}{927}e^{6} + \frac{1035241}{927}e^{5} - \frac{1258106}{927}e^{4} - \frac{1191760}{927}e^{3} + \frac{714682}{927}e^{2} + \frac{120410}{309}e - \frac{35426}{309}$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-1$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{1016}{309}e^{11} - \frac{6353}{309}e^{10} + \frac{1109}{103}e^{9} + \frac{81644}{309}e^{8} + \frac{78320}{309}e^{7} - \frac{273830}{309}e^{6} - \frac{313589}{309}e^{5} + \frac{381826}{309}e^{4} + \frac{355679}{309}e^{3} - \frac{218861}{309}e^{2} - \frac{35392}{103}e + \frac{10586}{103}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{222}{103}e^{11} - \frac{1362}{103}e^{10} + \frac{818}{103}e^{9} + \frac{17550}{103}e^{8} + \frac{16037}{103}e^{7} - \frac{59161}{103}e^{6} - \frac{65693}{103}e^{5} + \frac{82306}{103}e^{4} + \frac{75020}{103}e^{3} - \frac{46881}{103}e^{2} - \frac{22135}{103}e + \frac{6921}{103}$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $\phantom{-}\frac{740}{927}e^{11} + \frac{4952}{927}e^{10} - \frac{268}{309}e^{9} - \frac{61178}{927}e^{8} - \frac{74915}{927}e^{7} + \frac{185942}{927}e^{6} + \frac{264125}{927}e^{5} - \frac{238990}{927}e^{4} - \frac{273791}{927}e^{3} + \frac{133919}{927}e^{2} + \frac{24274}{309}e - \frac{6454}{309}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1270}{309}e^{11} + \frac{7864}{309}e^{10} - \frac{1515}{103}e^{9} - \frac{101746}{309}e^{8} - \frac{93883}{309}e^{7} + \frac{346768}{309}e^{6} + \frac{386347}{309}e^{5} - \frac{490724}{309}e^{4} - \frac{448384}{309}e^{3} + \frac{284005}{309}e^{2} + \frac{46197}{103}e - \frac{14108}{103}$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $-\frac{1879}{927}e^{11} - \frac{11617}{927}e^{10} + \frac{2147}{309}e^{9} + \frac{148846}{927}e^{8} + \frac{141274}{927}e^{7} - \frac{494197}{927}e^{6} - \frac{569113}{927}e^{5} + \frac{671117}{927}e^{4} + \frac{645892}{927}e^{3} - \frac{364645}{927}e^{2} - \frac{65447}{309}e + \frac{16190}{309}$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $-\frac{568}{309}e^{11} - \frac{3649}{309}e^{10} + \frac{444}{103}e^{9} + \frac{46225}{309}e^{8} + \frac{50554}{309}e^{7} - \frac{149035}{309}e^{6} - \frac{197581}{309}e^{5} + \frac{195659}{309}e^{4} + \frac{226642}{309}e^{3} - \frac{106246}{309}e^{2} - \frac{23297}{103}e + \frac{5112}{103}$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{601}{309}e^{11} - \frac{3793}{309}e^{10} + \frac{633}{103}e^{9} + \frac{49243}{309}e^{8} + \frac{48385}{309}e^{7} - \frac{169297}{309}e^{6} - \frac{201574}{309}e^{5} + \frac{242858}{309}e^{4} + \frac{242398}{309}e^{3} - \frac{146758}{309}e^{2} - \frac{26187}{103}e + \frac{8190}{103}$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $-\frac{1184}{927}e^{11} - \frac{7367}{927}e^{10} + \frac{1294}{309}e^{9} + \frac{94733}{927}e^{8} + \frac{92981}{927}e^{7} - \frac{316418}{927}e^{6} - \frac{385520}{927}e^{5} + \frac{425953}{927}e^{4} + \frac{460499}{927}e^{3} - \frac{227990}{927}e^{2} - \frac{49159}{309}e + \frac{10450}{309}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $-\frac{2077}{309}e^{11} - \frac{12790}{309}e^{10} + \frac{2663}{103}e^{9} + \frac{166645}{309}e^{8} + \frac{147109}{309}e^{7} - \frac{577453}{309}e^{6} - \frac{615628}{309}e^{5} + \frac{830402}{309}e^{4} + \frac{714472}{309}e^{3} - \frac{484735}{309}e^{2} - \frac{71766}{103}e + \frac{23328}{103}$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $-\frac{2318}{309}e^{11} - \frac{14366}{309}e^{10} + \frac{2826}{103}e^{9} + \frac{186560}{309}e^{8} + \frac{169154}{309}e^{7} - \frac{641585}{309}e^{6} - \frac{698555}{309}e^{5} + \frac{916858}{309}e^{4} + \frac{807431}{309}e^{3} - \frac{533489}{309}e^{2} - \frac{81960}{103}e + \frac{26115}{103}$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $\phantom{-}\frac{262}{927}e^{11} + \frac{1162}{927}e^{10} - \frac{1229}{309}e^{9} - \frac{20122}{927}e^{8} + \frac{11696}{927}e^{7} + \frac{111016}{927}e^{6} + \frac{10999}{927}e^{5} - \frac{223490}{927}e^{4} - \frac{50905}{927}e^{3} + \frac{156307}{927}e^{2} + \frac{8915}{309}e - \frac{6890}{309}$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $-\frac{1598}{309}e^{11} - \frac{9932}{309}e^{10} + \frac{1886}{103}e^{9} + \frac{128831}{309}e^{8} + \frac{119564}{309}e^{7} - \frac{441143}{309}e^{6} - \frac{495251}{309}e^{5} + \frac{622594}{309}e^{4} + \frac{575297}{309}e^{3} - \frac{356639}{309}e^{2} - \frac{58111}{103}e + \frac{17575}{103}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $-\frac{107}{103}e^{11} - \frac{701}{103}e^{10} + \frac{256}{103}e^{9} + \frac{9074}{103}e^{8} + \frac{9597}{103}e^{7} - \frac{30987}{103}e^{6} - \frac{38491}{103}e^{5} + \frac{44318}{103}e^{4} + \frac{45123}{103}e^{3} - \frac{27402}{103}e^{2} - \frac{14263}{103}e + \frac{4846}{103}$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $\phantom{-}\frac{1904}{309}e^{11} + \frac{11801}{309}e^{10} - \frac{2234}{103}e^{9} - \frac{152462}{309}e^{8} - \frac{142262}{309}e^{7} + \frac{517478}{309}e^{6} + \frac{584807}{309}e^{5} - \frac{727015}{309}e^{4} - \frac{679964}{309}e^{3} + \frac{418745}{309}e^{2} + \frac{70330}{103}e - \frac{20638}{103}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{876}{103}e^{11} - \frac{5405}{103}e^{10} + \frac{3225}{103}e^{9} + \frac{70067}{103}e^{8} + \frac{63785}{103}e^{7} - \frac{239782}{103}e^{6} - \frac{264513}{103}e^{5} + \frac{339749}{103}e^{4} + \frac{306645}{103}e^{3} - \frac{196164}{103}e^{2} - \frac{93131}{103}e + \frac{28802}{103}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $1$ |