Base field 4.4.9301.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 5 x^2 + x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[15, 15, -w^2 + 2 w + 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^3 - 4 x^2 - 2 x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w^3 + w^2 + 4 w + 1]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^2 + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^2 + w + 2]$ | $\phantom{-}e^2 - 4 e - 2$ |
| 16 | $[16, 2, 2]$ | $-e^2 + e + 7$ |
| 17 | $[17, 17, -w^3 + w^2 + 4 w - 2]$ | $-e + 4$ |
| 23 | $[23, 23, -w^3 + 2 w^2 + 3 w - 2]$ | $\phantom{-}e^2 - 2 e - 2$ |
| 27 | $[27, 3, -w^3 + w^2 + 5 w - 1]$ | $-2 e^2 + 8 e + 4$ |
| 37 | $[37, 37, -w^3 + 4 w + 1]$ | $-e^2 + 4 e + 4$ |
| 37 | $[37, 37, -w^3 + w^2 + 2 w + 1]$ | $\phantom{-}2 e^2 - 8 e - 4$ |
| 49 | $[49, 7, -w^3 + 3 w^2 + 2 w - 4]$ | $\phantom{-}4 e^2 - 14 e - 6$ |
| 61 | $[61, 61, -w^3 + 2 w^2 + 4 w - 2]$ | $-4 e^2 + 17 e + 6$ |
| 61 | $[61, 61, -w^3 + 3 w^2 + 2 w - 7]$ | $-2 e^2 + 6 e + 10$ |
| 67 | $[67, 67, w^2 - 3 w - 2]$ | $\phantom{-}e^2 - 5 e$ |
| 71 | $[71, 71, -w^2 + 5]$ | $-e^2 + 4 e - 6$ |
| 71 | $[71, 71, 2 w^3 - w^2 - 9 w - 2]$ | $\phantom{-}2 e^2 - 10 e + 2$ |
| 71 | $[71, 71, w^2 - 2 w - 5]$ | $-e^2 + 4 e - 6$ |
| 79 | $[79, 79, w^2 - 3 w - 1]$ | $-4 e^2 + 16 e + 10$ |
| 79 | $[79, 79, w^3 - 6 w - 1]$ | $\phantom{-}2 e^2 - 9 e + 2$ |
| 89 | $[89, 89, -w^3 + 3 w^2 + 3 w - 7]$ | $-5 e^2 + 18 e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |
| $5$ | $[5, 5, -w^3 + w^2 + 4 w + 1]$ | $-1$ |