Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 12 x^2 + 13 x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19,19,-w + 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^3 - 4 x^2 - 12 x + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^3 + 8 w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2} e^2 + e + 5$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}e - 3$ |
| 19 | $[19, 19, -w^2 + 6]$ | $-\frac{1}{6} e^2 + \frac{5}{3} e - 1$ |
| 19 | $[19, 19, -w^2 + 2 w + 5]$ | $-\frac{1}{2} e^2 + 9$ |
| 19 | $[19, 19, -w + 2]$ | $-1$ |
| 25 | $[25, 5, 2 w^2 - 2 w - 13]$ | $-\frac{1}{3} e^2 + \frac{1}{3} e + 1$ |
| 29 | $[29, 29, -w^2 + 9]$ | $\phantom{-}\frac{1}{3} e^2 - \frac{1}{3} e - 5$ |
| 29 | $[29, 29, -w^2 + 2 w + 6]$ | $-\frac{1}{3} e^2 - \frac{2}{3} e + 2$ |
| 29 | $[29, 29, w^2 - 7]$ | $\phantom{-}4$ |
| 29 | $[29, 29, -w^2 + 2 w + 8]$ | $\phantom{-}e - 2$ |
| 31 | $[31, 31, -2 w^2 + w + 12]$ | $\phantom{-}2 e - 2$ |
| 31 | $[31, 31, 2 w^2 - 3 w - 11]$ | $-\frac{1}{2} e^2 + 7$ |
| 41 | $[41, 41, -w]$ | $-\frac{1}{3} e^2 - \frac{2}{3} e + 6$ |
| 41 | $[41, 41, -w + 1]$ | $\phantom{-}\frac{1}{6} e^2 + \frac{4}{3} e - 3$ |
| 49 | $[49, 7, w^3 + 2 w^2 - 10 w - 20]$ | $\phantom{-}\frac{2}{3} e^2 + \frac{1}{3} e - 14$ |
| 49 | $[49, 7, w^3 - 5 w^2 - 3 w + 27]$ | $-\frac{1}{3} e^2 + \frac{4}{3} e + 2$ |
| 61 | $[61, 61, 2 w^2 - 3 w - 14]$ | $-\frac{2}{3} e^2 + \frac{5}{3} e$ |
| 61 | $[61, 61, 2 w^2 - w - 15]$ | $-\frac{1}{3} e^2 + \frac{7}{3} e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w + 2]$ | $1$ |