Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 10, w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 7x^{3} + 3x^{2} + 58x - 92\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{2} - w - 5]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{9}{2}e - 9$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + \frac{7}{2}e - 18$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ | $\phantom{-}e^{3} - 4e^{2} - 9e + 34$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{11}{2}e^{2} - \frac{29}{2}e + 44$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $-e^{2} + 10$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ | $-e^{3} + 5e^{2} + 8e - 42$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{13}{2}e - 15$ |
| 41 | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{21}{2}e^{2} - \frac{45}{2}e + 87$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e^{2} + \frac{3}{2}e - 26$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ | $-\frac{3}{2}e^{3} + \frac{9}{2}e^{2} + \frac{29}{2}e - 33$ |
| 41 | $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + \frac{13}{2}e - 24$ |
| 79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{21}{2}e^{2} - \frac{37}{2}e + 77$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ | $-\frac{5}{2}e^{3} + \frac{19}{2}e^{2} + \frac{39}{2}e - 72$ |
| 79 | $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ | $-\frac{7}{2}e^{3} + \frac{29}{2}e^{2} + \frac{57}{2}e - 115$ |
| 79 | $[79, 79, w^{3} - w^{2} - 6w + 9]$ | $\phantom{-}\frac{7}{2}e^{3} - \frac{27}{2}e^{2} - \frac{59}{2}e + 102$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}0$ |
| 109 | $[109, 109, w^{2} - w - 7]$ | $\phantom{-}e^{3} - 3e^{2} - 12e + 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $-1$ |
| $5$ | $[5, 5, w^{2} - w - 5]$ | $-1$ |