Base field 6.6.1416125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 9x^{3} + 6x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 3x^{4} - 20x^{3} - 56x^{2} + 92x + 248\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $-\frac{3}{2}e^{4} - \frac{1}{2}e^{3} + 32e^{2} + e - 148$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{9}{2}e^{2} + e - 18$ |
| 19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ | $-\frac{5}{2}e^{4} - \frac{3}{2}e^{3} + 52e^{2} + 9e - 236$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ | $\phantom{-}\frac{9}{4}e^{4} + \frac{5}{4}e^{3} - \frac{93}{2}e^{2} - 7e + 206$ |
| 25 | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{3} + 4w + 1]$ | $-2e^{4} - e^{3} + 42e^{2} + 4e - 194$ |
| 41 | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $\phantom{-}\frac{5}{2}e^{4} + \frac{3}{2}e^{3} - 52e^{2} - 10e + 232$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ | $\phantom{-}\frac{15}{4}e^{4} + \frac{7}{4}e^{3} - \frac{159}{2}e^{2} - 10e + 362$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ | $\phantom{-}\frac{21}{4}e^{4} + \frac{9}{4}e^{3} - \frac{221}{2}e^{2} - 10e + 506$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 2w - 3]$ | $-\frac{5}{2}e^{4} - \frac{3}{2}e^{3} + 52e^{2} + 9e - 240$ |
| 61 | $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ | $\phantom{-}2e^{4} + e^{3} - 43e^{2} - 6e + 202$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{7}{2}e^{4} + \frac{1}{2}e^{3} - 76e^{2} + 4e + 359$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{1}{4}e^{3} - \frac{33}{2}e^{2} + 4e + 74$ |
| 71 | $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 8e^{2} - 4e + 18$ |
| 79 | $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ | $-\frac{3}{4}e^{4} - \frac{3}{4}e^{3} + \frac{29}{2}e^{2} + 6e - 60$ |
| 79 | $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ | $-\frac{5}{4}e^{4} - \frac{1}{4}e^{3} + \frac{53}{2}e^{2} - 116$ |
| 89 | $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ | $\phantom{-}\frac{5}{4}e^{4} + \frac{1}{4}e^{3} - \frac{55}{2}e^{2} + 128$ |
| 109 | $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ | $\phantom{-}\frac{23}{4}e^{4} + \frac{11}{4}e^{3} - \frac{245}{2}e^{2} - 13e + 568$ |
| 109 | $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ | $-2e^{4} - e^{3} + 42e^{2} + 6e - 198$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $-1$ |