Base field 4.4.13725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11,11,4w^{3} - 13w^{2} - 23w + 55]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 10x^{2} - 7x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -2w^{3} + 6w^{2} + 13w - 26]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{2} - w - 8]$ | $-2e^{3} + 3e^{2} + 19e + 7$ |
| 11 | $[11, 11, -4w^{3} + 13w^{2} + 23w - 55]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $-2e^{3} + 3e^{2} + 19e + 5$ |
| 19 | $[19, 19, -w - 1]$ | $-e^{3} + 2e^{2} + 7e - 1$ |
| 19 | $[19, 19, -w^{3} + 3w^{2} + 7w - 14]$ | $-2e^{3} + 3e^{2} + 20e + 5$ |
| 19 | $[19, 19, w^{3} - 4w^{2} - 5w + 20]$ | $\phantom{-}e^{3} - 2e^{2} - 9e - 2$ |
| 19 | $[19, 19, -3w^{3} + 10w^{2} + 17w - 43]$ | $-2e^{3} + 3e^{2} + 18e + 4$ |
| 25 | $[25, 5, -w^{3} + 3w^{2} + 6w - 10]$ | $-2e^{3} + 3e^{2} + 18e + 3$ |
| 29 | $[29, 29, 4w^{3} - 13w^{2} - 23w + 57]$ | $\phantom{-}2e^{3} - 2e^{2} - 20e - 10$ |
| 29 | $[29, 29, w^{2} - w - 6]$ | $-e^{3} + e^{2} + 11e + 10$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 11w - 31]$ | $\phantom{-}e^{3} - 13e - 8$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 11w - 32]$ | $\phantom{-}3e^{3} - 6e^{2} - 25e - 2$ |
| 41 | $[41, 41, 3w^{3} - 10w^{2} - 18w + 43]$ | $-8e^{3} + 12e^{2} + 72e + 26$ |
| 41 | $[41, 41, 3w^{3} - 9w^{2} - 19w + 37]$ | $-e^{2} + e + 3$ |
| 41 | $[41, 41, 2w^{3} - 6w^{2} - 11w + 24]$ | $\phantom{-}4e^{3} - 5e^{2} - 41e - 15$ |
| 41 | $[41, 41, -2w^{3} + 7w^{2} + 12w - 33]$ | $\phantom{-}2e^{3} - 4e^{2} - 14e$ |
| 59 | $[59, 59, 3w^{3} - 10w^{2} - 17w + 46]$ | $-2e^{3} + 3e^{2} + 19e + 9$ |
| 59 | $[59, 59, -w^{3} + 4w^{2} + 5w - 17]$ | $-8e^{3} + 12e^{2} + 74e + 24$ |
| 61 | $[61, 61, 4w^{3} - 12w^{2} - 25w + 50]$ | $\phantom{-}3e^{3} - 5e^{2} - 25e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,4w^{3} - 13w^{2} - 23w + 55]$ | $1$ |