Base field 4.4.9225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 10x^{2} + 7x + 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 30x^{2} + 72\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{3}{4}]$ | $\phantom{-}\frac{1}{6}e^{2} - 3$ |
| 4 | $[4, 2, \frac{1}{2}w^{3} - 4w - \frac{1}{2}]$ | $\phantom{-}\frac{1}{6}e^{2} - 3$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} + w^{2} - 3w - \frac{7}{2}]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{2}w + \frac{7}{4}]$ | $-\frac{1}{6}e^{3} + 4e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{3}{2}]$ | $-\frac{1}{6}e^{3} + 4e$ |
| 19 | $[19, 19, w]$ | $-\frac{1}{6}e^{2} + 2$ |
| 19 | $[19, 19, \frac{1}{4}w^{3} - \frac{5}{2}w + \frac{1}{4}]$ | $-\frac{1}{6}e^{2} + 2$ |
| 25 | $[25, 5, \frac{1}{2}w^{3} - 3w - \frac{1}{2}]$ | $-\frac{1}{6}e^{2} + 8$ |
| 29 | $[29, 29, \frac{3}{4}w^{3} + w^{2} - \frac{9}{2}w - \frac{25}{4}]$ | $\phantom{-}\frac{1}{6}e^{3} - 5e$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{9}{2}]$ | $\phantom{-}\frac{1}{6}e^{3} - 5e$ |
| 41 | $[41, 41, -w^{3} + 7w + 3]$ | $-\frac{1}{6}e^{3} + 7e$ |
| 41 | $[41, 41, -\frac{3}{4}w^{3} + \frac{11}{2}w - \frac{3}{4}]$ | $-e$ |
| 41 | $[41, 41, \frac{1}{4}w^{3} + w^{2} - \frac{5}{2}w - \frac{11}{4}]$ | $-e$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} - 4w + \frac{5}{2}]$ | $\phantom{-}\frac{1}{6}e^{3} - 6e$ |
| 71 | $[71, 71, \frac{3}{4}w^{3} + w^{2} - \frac{11}{2}w - \frac{21}{4}]$ | $\phantom{-}\frac{1}{6}e^{3} - 6e$ |
| 79 | $[79, 79, \frac{1}{4}w^{3} - 2w^{2} + \frac{1}{2}w + \frac{25}{4}]$ | $\phantom{-}\frac{1}{6}e^{2} - 6$ |
| 79 | $[79, 79, -\frac{3}{4}w^{3} + \frac{13}{2}w + \frac{9}{4}]$ | $\phantom{-}\frac{1}{6}e^{2} - 6$ |
| 89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{41}{4}]$ | $\phantom{-}\frac{1}{3}e^{3} - 7e$ |
| 89 | $[89, 89, -\frac{7}{4}w^{3} - w^{2} + \frac{27}{2}w + \frac{33}{4}]$ | $\phantom{-}\frac{1}{3}e^{3} - 7e$ |
| 101 | $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{1}{2}w - \frac{27}{4}]$ | $\phantom{-}\frac{1}{6}e^{3} - 3e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).