Base field 4.4.5225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + x + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{3} + 2w^{2} + 4w - 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 22x^{6} + 153x^{4} - 356x^{2} + 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 3w - \frac{7}{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w + 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{5}{2}]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{13}{4}e^{3} + 8e$ |
| 19 | $[19, 19, -\frac{1}{2}w^{3} + 3w + \frac{3}{2}]$ | $-\frac{1}{4}e^{6} + \frac{17}{4}e^{4} - 19e^{2} + 16$ |
| 25 | $[25, 5, -w^{3} + 2w^{2} + 4w - 4]$ | $-1$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 5w + 3]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{9}{4}e^{5} + \frac{85}{8}e^{3} - \frac{21}{2}e$ |
| 31 | $[31, 31, -\frac{1}{2}w^{3} + w^{2} + w - \frac{1}{2}]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{9}{4}e^{5} + \frac{85}{8}e^{3} - \frac{21}{2}e$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{15}{2}]$ | $-\frac{1}{4}e^{6} + \frac{17}{4}e^{4} - 17e^{2} + 6$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - w^{2} - 4w - \frac{5}{2}]$ | $-\frac{1}{4}e^{6} + \frac{17}{4}e^{4} - 17e^{2} + 6$ |
| 61 | $[61, 61, -2w^{3} + 5w^{2} + 8w - 12]$ | $-\frac{1}{8}e^{7} + \frac{5}{2}e^{5} - \frac{119}{8}e^{3} + \frac{47}{2}e$ |
| 61 | $[61, 61, \frac{1}{2}w^{3} - 2w - \frac{5}{2}]$ | $-\frac{1}{8}e^{7} + \frac{5}{2}e^{5} - \frac{119}{8}e^{3} + \frac{47}{2}e$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} - \frac{15}{2}]$ | $-\frac{1}{4}e^{6} + \frac{7}{2}e^{4} - \frac{37}{4}e^{2} - 6$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} - 4w^{2} - 5w + \frac{23}{2}]$ | $-\frac{1}{4}e^{6} + \frac{7}{2}e^{4} - \frac{37}{4}e^{2} - 6$ |
| 79 | $[79, 79, -\frac{5}{2}w^{3} + 6w^{2} + 9w - \frac{31}{2}]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{15}{4}e^{4} + \frac{21}{2}e^{2} + 10$ |
| 79 | $[79, 79, -4w^{3} + 10w^{2} + 17w - 28]$ | $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - 16e$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 4w + 1]$ | $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - 16e$ |
| 79 | $[79, 79, \frac{5}{2}w^{3} - 6w^{2} - 9w + \frac{23}{2}]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{15}{4}e^{4} + \frac{21}{2}e^{2} + 10$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{4}e^{6} + 5e^{4} - \frac{103}{4}e^{2} + 25$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{3} + 2w^{2} + 4w - 4]$ | $1$ |