Base field 4.4.1957.1
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[73, 73, 2w^{2} - w - 5]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 14x^{4} - 2x^{3} + 32x^{2} + 16x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 3w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}4e^{5} - e^{4} - 56e^{3} + 6e^{2} + 128e + 32$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}4e^{5} - e^{4} - 56e^{3} + 6e^{2} + 130e + 33$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $\phantom{-}e^{5} - 14e^{3} - 2e^{2} + 33e + 14$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 2]$ | $-8e^{5} + 2e^{4} + 111e^{3} - 12e^{2} - 249e - 62$ |
| 27 | $[27, 3, -2w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}7e^{5} - 2e^{4} - 97e^{3} + 14e^{2} + 215e + 50$ |
| 31 | $[31, 31, -w^{3} + 5w]$ | $-2e^{5} + 28e^{3} + 3e^{2} - 64e - 22$ |
| 37 | $[37, 37, -w^{3} + 5w + 1]$ | $\phantom{-}2e^{5} - 28e^{3} - 4e^{2} + 66e + 26$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $\phantom{-}2e^{5} - 28e^{3} - 3e^{2} + 64e + 24$ |
| 43 | $[43, 43, -w^{2} + 2w + 3]$ | $-8e^{5} + 2e^{4} + 112e^{3} - 12e^{2} - 258e - 70$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 2w + 2]$ | $-7e^{5} + 2e^{4} + 97e^{3} - 14e^{2} - 215e - 48$ |
| 47 | $[47, 47, 3w^{3} - w^{2} - 10w - 2]$ | $\phantom{-}6e^{5} - 2e^{4} - 84e^{3} + 15e^{2} + 192e + 42$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 2w - 3]$ | $-14e^{5} + 4e^{4} + 195e^{3} - 26e^{2} - 443e - 108$ |
| 59 | $[59, 59, -2w^{3} + w^{2} + 8w + 1]$ | $-e^{2} - 2e + 10$ |
| 59 | $[59, 59, w^{3} - 2w^{2} - 3w + 3]$ | $-8e^{5} + 2e^{4} + 112e^{3} - 12e^{2} - 256e - 62$ |
| 61 | $[61, 61, -w^{3} + w^{2} + w - 2]$ | $-2e - 4$ |
| 67 | $[67, 67, 2w^{3} - 5w - 2]$ | $\phantom{-}14e^{5} - 4e^{4} - 194e^{3} + 28e^{2} + 432e + 104$ |
| 71 | $[71, 71, 2w^{2} - w - 3]$ | $-10e^{5} + 2e^{4} + 140e^{3} - 10e^{2} - 322e - 80$ |
| 73 | $[73, 73, 2w^{2} - w - 5]$ | $-1$ |
| 73 | $[73, 73, w^{3} - 2w^{2} - 2w + 5]$ | $-3e^{5} + 42e^{3} + 4e^{2} - 97e - 32$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $73$ | $[73, 73, 2w^{2} - w - 5]$ | $1$ |