Base field 4.4.4352.1
Generator \(w\), with minimal polynomial \(x^4 - 6 x^2 - 4 x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[41, 41, w^3 - 3 w^2 - 2 w + 7]$ |
| Dimension: | $8$ |
| 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:
| \(x^8 - 28 x^6 + 270 x^4 - 1038 x^2 + 1376\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}\frac{1}{2} e^6 - 12 e^4 + 88 e^2 - 182$ |
| 7 | $[7, 7, -w^3 + w^2 + 5 w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{1}{4} e^7 - 6 e^5 + \frac{89}{2} e^3 - \frac{191}{2} e$ |
| 17 | $[17, 17, -w^3 + 2 w^2 + 4 w - 3]$ | $\phantom{-}e^4 - 14 e^2 + 38$ |
| 23 | $[23, 23, -2 w^3 + 2 w^2 + 9 w + 1]$ | $\phantom{-}e^7 - 25 e^5 + 191 e^3 - 409 e$ |
| 23 | $[23, 23, -w^3 + w^2 + 3 w + 1]$ | $\phantom{-}\frac{1}{4} e^7 - 6 e^5 + \frac{89}{2} e^3 - \frac{187}{2} e$ |
| 31 | $[31, 31, w^2 - w - 1]$ | $-\frac{3}{2} e^7 + 36 e^5 - 265 e^3 + 553 e$ |
| 31 | $[31, 31, w^3 - 2 w^2 - 3 w + 5]$ | $\phantom{-}\frac{3}{4} e^7 - 18 e^5 + \frac{265}{2} e^3 - \frac{555}{2} e$ |
| 41 | $[41, 41, w^3 - 3 w^2 - 2 w + 7]$ | $-1$ |
| 41 | $[41, 41, w^3 - 3 w^2 - 2 w + 5]$ | $-e^4 + 15 e^2 - 42$ |
| 49 | $[49, 7, 2 w^3 - 2 w^2 - 8 w - 1]$ | $-2 e^6 + 50 e^4 - 383 e^2 + 826$ |
| 71 | $[71, 71, -2 w^3 + 3 w^2 + 8 w - 1]$ | $\phantom{-}\frac{3}{2} e^7 - 37 e^5 + 279 e^3 - 588 e$ |
| 71 | $[71, 71, w^2 - 5]$ | $-\frac{7}{4} e^7 + 43 e^5 - \frac{647}{2} e^3 + \frac{1377}{2} e$ |
| 73 | $[73, 73, -3 w^3 + 4 w^2 + 11 w - 3]$ | $-3 e^6 + 75 e^4 - 574 e^2 + 1234$ |
| 73 | $[73, 73, 2 w^3 - w^2 - 9 w - 3]$ | $-e^6 + 24 e^4 - 176 e^2 + 374$ |
| 79 | $[79, 79, 3 w^3 - 4 w^2 - 13 w + 3]$ | $-e^7 + 25 e^5 - 192 e^3 + 416 e$ |
| 79 | $[79, 79, w^2 + w - 3]$ | $\phantom{-}\frac{3}{2} e^7 - 36 e^5 + 265 e^3 - 553 e$ |
| 81 | $[81, 3, -3]$ | $-2 e^6 + 47 e^4 - 340 e^2 + 706$ |
| 89 | $[89, 89, -w^3 + 3 w^2 + 3 w - 11]$ | $\phantom{-}7 e^6 - 171 e^4 + 1280 e^2 - 2706$ |
| 89 | $[89, 89, 3 w^3 - 2 w^2 - 14 w - 3]$ | $-2 e^6 + 49 e^4 - 368 e^2 + 782$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, w^3 - 3 w^2 - 2 w + 7]$ | $1$ |