Base field 4.4.16225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 6x + 36\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[36,6,-w^{2} + w + 4]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 3x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ | $-1$ |
| 4 | $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ | $\phantom{-}2$ |
| 9 | $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ | $-1$ |
| 11 | $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ | $\phantom{-}2$ |
| 19 | $[19, 19, w + 1]$ | $-2e + 2$ |
| 19 | $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ | $-2$ |
| 25 | $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ | $\phantom{-}2$ |
| 29 | $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ | $\phantom{-}3e - 5$ |
| 29 | $[29, 29, w - 1]$ | $\phantom{-}e + 1$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ | $-3e + 7$ |
| 31 | $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ | $\phantom{-}e + 3$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ | $\phantom{-}e + 3$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ | $-e + 7$ |
| 59 | $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $-e + 1$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ | $-2e + 4$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ | $\phantom{-}4e$ |
| 79 | $[79, 79, w^{2} - 11]$ | $\phantom{-}8$ |
| 79 | $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ | $-e - 1$ |
| 89 | $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ | $-4e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,-\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{4}{3}w - 6]$ | $1$ |
| $9$ | $[9,3,-\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 5]$ | $1$ |