Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 15 x^2 + 2 x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $67$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 + 3 x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + \frac{9}{2} w - 10]$ | $\phantom{-}e + 2$ |
| 9 | $[9, 3, \frac{1}{2} w^3 - \frac{5}{2} w^2 - \frac{5}{2} w + 17]$ | $\phantom{-}4 e + 5$ |
| 9 | $[9, 3, \frac{3}{2} w^3 - \frac{11}{2} w^2 - \frac{19}{2} w + 28]$ | $-3$ |
| 11 | $[11, 11, \frac{1}{2} w^3 - \frac{3}{2} w^2 - \frac{9}{2} w + 11]$ | $-3 e - 5$ |
| 11 | $[11, 11, -w - 3]$ | $-e - 3$ |
| 25 | $[25, 5, w^3 - 3 w^2 - 7 w + 15]$ | $\phantom{-}e + 2$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, \frac{1}{2} w^3 - \frac{3}{2} w^2 - \frac{9}{2} w + 9]$ | $\phantom{-}6 e + 8$ |
| 31 | $[31, 31, -\frac{1}{2} w^3 + \frac{5}{2} w^2 + \frac{5}{2} w - 16]$ | $\phantom{-}3$ |
| 31 | $[31, 31, \frac{1}{2} w^3 - \frac{3}{2} w^2 - \frac{9}{2} w + 5]$ | $-3$ |
| 31 | $[31, 31, -w + 3]$ | $\phantom{-}2 e + 3$ |
| 31 | $[31, 31, \frac{3}{2} w^3 - \frac{11}{2} w^2 - \frac{19}{2} w + 29]$ | $-3$ |
| 59 | $[59, 59, 2 w^2 - w - 13]$ | $\phantom{-}4 e + 5$ |
| 59 | $[59, 59, \frac{9}{2} w^3 - \frac{31}{2} w^2 - \frac{61}{2} w + 85]$ | $\phantom{-}6 e + 5$ |
| 61 | $[61, 61, 2 w^3 - 6 w^2 - 15 w + 31]$ | $-5 e - 13$ |
| 61 | $[61, 61, -\frac{3}{2} w^3 + \frac{11}{2} w^2 + \frac{21}{2} w - 34]$ | $-13 e - 19$ |
| 71 | $[71, 71, \frac{3}{2} w^3 - \frac{11}{2} w^2 - \frac{19}{2} w + 32]$ | $-e + 6$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + \frac{5}{2} w^2 + \frac{5}{2} w - 13]$ | $\phantom{-}5 e + 6$ |
| 79 | $[79, 79, -3 w^3 + 10 w^2 + 19 w - 51]$ | $-9 e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w + 1]$ | $-1$ |