Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[21, 21, w^{2} - w - 6]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 3x^{5} - 11x^{4} + 33x^{3} - 8x^{2} - 8x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}15e^{5} - 48e^{4} - 155e^{3} + 526e^{2} - 230e - 75$ |
| 13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $-12e^{5} + 38e^{4} + 125e^{3} - 416e^{2} + 173e + 58$ |
| 16 | $[16, 2, 2]$ | $-e^{5} + 3e^{4} + 11e^{3} - 33e^{2} + 7e + 6$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}10e^{5} - 32e^{4} - 104e^{3} + 351e^{2} - 146e - 52$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $-3e^{5} + 10e^{4} + 30e^{3} - 110e^{2} + 57e + 15$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $\phantom{-}41e^{5} - 132e^{4} - 423e^{3} + 1447e^{2} - 634e - 199$ |
| 31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}34e^{5} - 109e^{4} - 351e^{3} + 1194e^{2} - 523e - 165$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $-4e^{5} + 12e^{4} + 43e^{3} - 131e^{2} + 45e + 20$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $-14e^{5} + 45e^{4} + 145e^{3} - 493e^{2} + 209e + 70$ |
| 43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $-11e^{5} + 36e^{4} + 112e^{3} - 395e^{2} + 186e + 52$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $-47e^{5} + 152e^{4} + 483e^{3} - 1667e^{2} + 746e + 229$ |
| 53 | $[53, 53, -w - 3]$ | $-20e^{5} + 65e^{4} + 205e^{3} - 714e^{2} + 322e + 99$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $-9e^{5} + 29e^{4} + 92e^{3} - 317e^{2} + 148e + 36$ |
| 59 | $[59, 59, 2w^{2} - 3w - 6]$ | $-3e^{5} + 9e^{4} + 33e^{3} - 99e^{2} + 25e + 17$ |
| 59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $\phantom{-}7e^{5} - 22e^{4} - 73e^{3} + 240e^{2} - 103e - 28$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $\phantom{-}e^{3} - e^{2} - 11e + 6$ |
| 79 | $[79, 79, w^{2} - 2w - 1]$ | $-18e^{5} + 57e^{4} + 188e^{3} - 625e^{2} + 256e + 91$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $1$ |
| $7$ | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $-1$ |