Base field 4.4.4525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 3x + 9\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[45, 15, -w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 13x^{2} - 3x + 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ | $-1$ |
| 5 | $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w]$ | $-1$ |
| 9 | $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{7}{3}e + 6$ |
| 16 | $[16, 2, 2]$ | $-e^{2} + e + 5$ |
| 19 | $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ | $-\frac{2}{3}e^{3} + \frac{5}{3}e^{2} + \frac{20}{3}e - 4$ |
| 19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{1}{3}e + 8$ |
| 31 | $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 4$ |
| 31 | $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ | $-e^{3} + 2e^{2} + 8e - 2$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ | $-\frac{1}{3}e^{3} - \frac{2}{3}e^{2} + \frac{16}{3}e + 2$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{2}{3}e^{2} - \frac{20}{3}e - 4$ |
| 61 | $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ | $-\frac{4}{3}e^{3} + \frac{7}{3}e^{2} + \frac{40}{3}e$ |
| 61 | $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{5}{3}e^{2} - \frac{20}{3}e + 6$ |
| 71 | $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ | $-\frac{2}{3}e^{3} + \frac{8}{3}e^{2} + \frac{14}{3}e - 14$ |
| 71 | $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{19}{3}e + 10$ |
| 89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ | $\phantom{-}e + 6$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{1}{3}e^{2} - \frac{26}{3}e - 10$ |
| 101 | $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ | $\phantom{-}e^{3} - 2e^{2} - 9e + 12$ |
| 101 | $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ | $\phantom{-}e^{3} - e^{2} - 9e$ |
| 101 | $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{4}{3}e^{2} - \frac{1}{3}e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ | $1$ |
| $9$ | $[9, 3, -w]$ | $1$ |