Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $63$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 4x^{5} - 11x^{4} + 42x^{3} + 39x^{2} - 99x - 27\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 3e + 3$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ | $-\frac{1}{3}e^{4} + e^{3} + \frac{4}{3}e^{2} - 4e + 4$ |
| 9 | $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ | $\phantom{-}e^{2} - e - 5$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 4e - 2$ |
| 11 | $[11, 11, -w - 3]$ | $-\frac{1}{3}e^{4} + e^{3} + \frac{4}{3}e^{2} - 3e + 4$ |
| 25 | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $-1$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{13}{3}e^{2} - 2e + 9$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - \frac{11}{3}e^{2} + 2e + 6$ |
| 31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{1}{3}e^{2} - 6e - 1$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ | $\phantom{-}e + 1$ |
| 31 | $[31, 31, -w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 3e + 4$ |
| 31 | $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ | $-\frac{1}{3}e^{4} + \frac{4}{3}e^{3} + \frac{2}{3}e^{2} - 5e + 5$ |
| 59 | $[59, 59, 2w^{2} - w - 13]$ | $\phantom{-}2e^{2} - 3e - 8$ |
| 59 | $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ | $-\frac{2}{3}e^{4} + \frac{5}{3}e^{3} + \frac{10}{3}e^{2} - 5e + 7$ |
| 61 | $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{14}{3}e^{3} + e^{2} + 16e + 1$ |
| 61 | $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ | $-\frac{1}{3}e^{5} + 2e^{4} - \frac{40}{3}e^{2} + 7e + 10$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ | $\phantom{-}\frac{2}{3}e^{4} - 3e^{3} - \frac{5}{3}e^{2} + 15e - 6$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ | $\phantom{-}\frac{1}{3}e^{4} - 2e^{3} - \frac{4}{3}e^{2} + 12e + 3$ |
| 79 | $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ | $-e^{4} + 2e^{3} + 8e^{2} - 7e - 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $1$ |