Base field 4.4.8768.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[31, 31, w^{2} - 5]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 5x^{5} - 2x^{4} - 42x^{3} - 52x^{2} + 22x + 45\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}2e^{5} + 7e^{4} - 15e^{3} - 62e^{2} - 7e + 58$ |
| 7 | $[7, 7, -w^{2} + 2w + 1]$ | $\phantom{-}2e^{5} + 6e^{4} - 16e^{3} - 53e^{2} + 48$ |
| 7 | $[7, 7, w^{2} - 2]$ | $-6e^{5} - 20e^{4} + 45e^{3} + 177e^{2} + 20e - 167$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}5e^{5} + 17e^{4} - 37e^{3} - 150e^{2} - 21e + 138$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}4e^{5} + 13e^{4} - 30e^{3} - 113e^{2} - 13e + 99$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}3e^{5} + 10e^{4} - 23e^{3} - 89e^{2} - 6e + 84$ |
| 31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -w^{2} + 2w + 4]$ | $\phantom{-}4e^{5} + 13e^{4} - 30e^{3} - 115e^{2} - 15e + 107$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ | $-4e^{5} - 15e^{4} + 28e^{3} + 133e^{2} + 27e - 128$ |
| 41 | $[41, 41, w^{3} - w^{2} - 3w - 3]$ | $-2e^{2} + e + 12$ |
| 47 | $[47, 47, w^{2} - 2w - 5]$ | $-12e^{5} - 41e^{4} + 89e^{3} + 364e^{2} + 49e - 342$ |
| 47 | $[47, 47, w^{2} - 6]$ | $\phantom{-}4e^{5} + 12e^{4} - 31e^{3} - 105e^{2} - 8e + 88$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}13e^{5} + 45e^{4} - 96e^{3} - 400e^{2} - 51e + 387$ |
| 71 | $[71, 71, -w^{3} + w^{2} + 4w - 3]$ | $-12e^{5} - 41e^{4} + 89e^{3} + 363e^{2} + 51e - 343$ |
| 79 | $[79, 79, -w - 3]$ | $\phantom{-}9e^{5} + 32e^{4} - 66e^{3} - 285e^{2} - 44e + 270$ |
| 79 | $[79, 79, w - 4]$ | $\phantom{-}5e^{5} + 18e^{4} - 35e^{3} - 159e^{2} - 33e + 140$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}3e^{5} + 11e^{4} - 21e^{3} - 101e^{2} - 22e + 107$ |
| 89 | $[89, 89, w^{2} - 3w - 2]$ | $\phantom{-}7e^{5} + 25e^{4} - 50e^{3} - 223e^{2} - 40e + 210$ |
| 89 | $[89, 89, w^{2} + w - 4]$ | $-7e^{5} - 22e^{4} + 55e^{3} + 192e^{2} + 9e - 165$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, w^{2} - 5]$ | $-1$ |