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: | $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $50$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 10x^{2} - 16x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{11}{3}e - \frac{8}{3}$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ | $-e - 2$ |
| 9 | $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ | $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{11}{3}e + \frac{2}{3}$ |
| 11 | $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ | $\phantom{-}2$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 5e - 4$ |
| 19 | $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{3}e^{2} - \frac{1}{3}e + \frac{14}{3}$ |
| 25 | $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ | $-\frac{1}{6}e^{3} - \frac{2}{3}e^{2} + \frac{1}{3}e + \frac{16}{3}$ |
| 29 | $[29, 29, w - 1]$ | $-\frac{1}{2}e^{3} + 5e + 2$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ | $-\frac{5}{6}e^{3} - \frac{5}{6}e^{2} + \frac{26}{3}e + \frac{17}{3}$ |
| 31 | $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ | $-\frac{1}{6}e^{3} - \frac{1}{6}e^{2} - \frac{2}{3}e + \frac{1}{3}$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 4e + 8$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 4e - 4$ |
| 59 | $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $-\frac{1}{6}e^{3} + \frac{1}{3}e^{2} + \frac{10}{3}e - \frac{20}{3}$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ | $\phantom{-}\frac{1}{2}e^{3} - 6e - 6$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{8}{3}e - \frac{8}{3}$ |
| 79 | $[79, 79, w^{2} - 11]$ | $-\frac{5}{6}e^{3} - \frac{4}{3}e^{2} + \frac{17}{3}e + \frac{26}{3}$ |
| 79 | $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ | $-\frac{7}{6}e^{3} - \frac{2}{3}e^{2} + \frac{31}{3}e + \frac{16}{3}$ |
| 89 | $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ | $-\frac{2}{3}e^{3} - \frac{5}{3}e^{2} + \frac{19}{3}e + \frac{16}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ | $-1$ |