Base field 4.4.4400.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[41,41,-w^{3} + 2w^{2} + 4w - 6]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 4x^{5} - 5x^{4} + 24x^{3} + 5x^{2} - 34x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-e^{5} + 2e^{4} + 9e^{3} - 5e^{2} - 19e - 4$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w - 4]$ | $\phantom{-}2e^{5} - 4e^{4} - 19e^{3} + 13e^{2} + 41e + 5$ |
| 11 | $[11, 11, w]$ | $-3e^{5} + 6e^{4} + 29e^{3} - 22e^{2} - 62e + 2$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ | $-2e^{5} + 4e^{4} + 19e^{3} - 14e^{2} - 38e - 1$ |
| 29 | $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ | $\phantom{-}6e^{5} - 13e^{4} - 54e^{3} + 47e^{2} + 111e - 3$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w - 2]$ | $-4e^{5} + 9e^{4} + 34e^{3} - 30e^{2} - 69e$ |
| 31 | $[31, 31, -w^{3} - w^{2} + 4w + 2]$ | $\phantom{-}7e^{5} - 16e^{4} - 59e^{3} + 54e^{2} + 118e + 4$ |
| 41 | $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ | $\phantom{-}5e^{5} - 10e^{4} - 47e^{3} + 34e^{2} + 98e + 4$ |
| 41 | $[41, 41, w^{3} - 5w + 2]$ | $-1$ |
| 49 | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ | $-e^{5} + 2e^{4} + 10e^{3} - 8e^{2} - 25e + 6$ |
| 49 | $[49, 7, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}e^{4} - 3e^{3} - 5e^{2} + 8e + 11$ |
| 59 | $[59, 59, -3w^{2} - w + 10]$ | $-16e^{5} + 35e^{4} + 141e^{3} - 119e^{2} - 293e - 8$ |
| 59 | $[59, 59, -3w^{2} + w + 10]$ | $-2e^{5} + 2e^{4} + 25e^{3} - 4e^{2} - 58e - 13$ |
| 61 | $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ | $-15e^{5} + 34e^{4} + 129e^{3} - 118e^{2} - 264e$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ | $\phantom{-}13e^{5} - 28e^{4} - 117e^{3} + 99e^{2} + 241e + 6$ |
| 71 | $[71, 71, 2w^{2} + w - 9]$ | $\phantom{-}2e^{4} - 6e^{3} - 11e^{2} + 20e + 13$ |
| 71 | $[71, 71, 2w^{2} - w - 9]$ | $\phantom{-}14e^{5} - 31e^{4} - 122e^{3} + 104e^{2} + 248e + 15$ |
| 81 | $[81, 3, -3]$ | $-13e^{5} + 28e^{4} + 116e^{3} - 97e^{2} - 236e - 8$ |
| 101 | $[101, 101, 2w^{2} - w - 10]$ | $\phantom{-}12e^{5} - 25e^{4} - 111e^{3} + 85e^{2} + 239e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41,41,-w^{3} + 2w^{2} + 4w - 6]$ | $1$ |