Base field 5.5.176281.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 3x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[25, 25, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 3x^{5} - 20x^{4} - 65x^{3} + 58x^{2} + 281x + 183\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-\frac{18}{163}e^{5} - \frac{42}{163}e^{4} + \frac{388}{163}e^{3} + \frac{857}{163}e^{2} - \frac{1724}{163}e - \frac{3148}{163}$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}\frac{9}{163}e^{5} + \frac{21}{163}e^{4} - \frac{194}{163}e^{3} - \frac{347}{163}e^{2} + \frac{862}{163}e + \frac{759}{163}$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}\frac{21}{163}e^{5} + \frac{49}{163}e^{4} - \frac{507}{163}e^{3} - \frac{1027}{163}e^{2} + \frac{2609}{163}e + \frac{3727}{163}$ |
| 23 | $[23, 23, -w^{4} + 5w^{2} + w - 4]$ | $\phantom{-}\frac{43}{163}e^{5} + \frac{46}{163}e^{4} - \frac{945}{163}e^{3} - \frac{1024}{163}e^{2} + \frac{4209}{163}e + \frac{4224}{163}$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $\phantom{-}\frac{4}{163}e^{5} - \frac{45}{163}e^{4} - \frac{50}{163}e^{3} + \frac{697}{163}e^{2} - \frac{124}{163}e - \frac{1673}{163}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{27}{163}e^{5} + \frac{63}{163}e^{4} - \frac{582}{163}e^{3} - \frac{1367}{163}e^{2} + \frac{2749}{163}e + \frac{5211}{163}$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $\phantom{-}\frac{67}{163}e^{5} + \frac{102}{163}e^{4} - \frac{1408}{163}e^{3} - \frac{2058}{163}e^{2} + \frac{5910}{163}e + \frac{7552}{163}$ |
| 41 | $[41, 41, w^{4} - w^{3} - 3w^{2} + w + 1]$ | $-\frac{64}{163}e^{5} - \frac{95}{163}e^{4} + \frac{1452}{163}e^{3} + \frac{2051}{163}e^{2} - \frac{7144}{163}e - \frac{9255}{163}$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 4w]$ | $-\frac{39}{163}e^{5} - \frac{91}{163}e^{4} + \frac{895}{163}e^{3} + \frac{1721}{163}e^{2} - \frac{4496}{163}e - \frac{6549}{163}$ |
| 61 | $[61, 61, -w^{4} + 6w^{2} + w - 4]$ | $-\frac{12}{163}e^{5} - \frac{28}{163}e^{4} + \frac{150}{163}e^{3} + \frac{517}{163}e^{2} + \frac{46}{163}e - \frac{1501}{163}$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 4w - 3]$ | $-\frac{7}{163}e^{5} + \frac{38}{163}e^{4} + \frac{169}{163}e^{3} - \frac{690}{163}e^{2} - \frac{1087}{163}e + \frac{1420}{163}$ |
| 71 | $[71, 71, w^{4} - 6w^{2} + 7]$ | $-\frac{22}{163}e^{5} + \frac{3}{163}e^{4} + \frac{438}{163}e^{3} + \frac{160}{163}e^{2} - \frac{1926}{163}e - \frac{1638}{163}$ |
| 73 | $[73, 73, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $\phantom{-}\frac{80}{163}e^{5} + \frac{78}{163}e^{4} - \frac{1652}{163}e^{3} - \frac{1871}{163}e^{2} + \frac{6974}{163}e + \frac{9083}{163}$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $-\frac{86}{163}e^{5} - \frac{92}{163}e^{4} + \frac{1890}{163}e^{3} + \frac{2211}{163}e^{2} - \frac{8744}{163}e - \frac{10404}{163}$ |
| 83 | $[83, 83, -w^{4} + 5w^{2} + 2w - 4]$ | $\phantom{-}\frac{104}{163}e^{5} + \frac{134}{163}e^{4} - \frac{2278}{163}e^{3} - \frac{2905}{163}e^{2} + \frac{10468}{163}e + \frac{12411}{163}$ |
| 83 | $[83, 83, w^{4} - 5w^{2} + 2]$ | $-\frac{25}{163}e^{5} - \frac{4}{163}e^{4} + \frac{557}{163}e^{3} + \frac{4}{163}e^{2} - \frac{2811}{163}e + \frac{228}{163}$ |
| 89 | $[89, 89, -2w^{4} + 2w^{3} + 9w^{2} - 6w - 4]$ | $-\frac{43}{163}e^{5} - \frac{46}{163}e^{4} + \frac{945}{163}e^{3} + \frac{1024}{163}e^{2} - \frac{4535}{163}e - \frac{4224}{163}$ |
| 101 | $[101, 101, -2w^{4} + 2w^{3} + 8w^{2} - 3w - 3]$ | $\phantom{-}\frac{28}{163}e^{5} + \frac{11}{163}e^{4} - \frac{676}{163}e^{3} - \frac{337}{163}e^{2} + \frac{3370}{163}e + \frac{2307}{163}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $1$ |