Base field 3.3.1384.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} - w + 11]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 12x^{8} + 44x^{6} - 49x^{4} + 19x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w^{2} + 2w - 5]$ | $\phantom{-}e^{4} - 6e^{2} + 3$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $-2e^{9} + 23e^{7} - 77e^{5} + 63e^{3} - 11e$ |
| 11 | $[11, 11, -w^{2} - w + 11]$ | $-1$ |
| 11 | $[11, 11, 2w^{2} + 2w - 15]$ | $\phantom{-}4e^{9} - 46e^{7} + 153e^{5} - 120e^{3} + 19e$ |
| 11 | $[11, 11, w^{2} + w - 9]$ | $\phantom{-}3e^{9} - 35e^{7} + 121e^{5} - 112e^{3} + 29e$ |
| 13 | $[13, 13, 2w - 5]$ | $-3e^{9} + 35e^{7} - 120e^{5} + 106e^{3} - 27e$ |
| 17 | $[17, 17, -w^{2} - w + 5]$ | $-2e^{9} + 23e^{7} - 78e^{5} + 69e^{3} - 16e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}2e^{8} - 22e^{6} + 67e^{4} - 37e^{2}$ |
| 29 | $[29, 29, w^{2} + w - 3]$ | $-3e^{8} + 34e^{6} - 112e^{4} + 90e^{2} - 18$ |
| 37 | $[37, 37, -2w^{2} + 15]$ | $-2e^{9} + 23e^{7} - 75e^{5} + 52e^{3} - 10e$ |
| 43 | $[43, 43, 3w^{2} + w - 27]$ | $\phantom{-}e^{6} - 10e^{4} + 26e^{2} - 10$ |
| 49 | $[49, 7, -w^{2} + w + 3]$ | $-e^{7} + 12e^{5} - 42e^{3} + 34e$ |
| 67 | $[67, 67, 2w^{2} + 2w - 17]$ | $\phantom{-}2e^{9} - 21e^{7} + 54e^{5} + 10e^{3} - 27e$ |
| 71 | $[71, 71, 2w - 1]$ | $\phantom{-}e^{8} - 13e^{6} + 55e^{4} - 81e^{2} + 24$ |
| 79 | $[79, 79, 3w^{2} + w - 25]$ | $-7e^{9} + 80e^{7} - 261e^{5} + 185e^{3} - 18e$ |
| 83 | $[83, 83, w^{2} + 3w - 5]$ | $\phantom{-}3e^{8} - 35e^{6} + 120e^{4} - 105e^{2} + 16$ |
| 89 | $[89, 89, -4w^{2} - 4w + 31]$ | $\phantom{-}2e^{9} - 21e^{7} + 53e^{5} + 17e^{3} - 34e$ |
| 89 | $[89, 89, -2w^{2} + 17]$ | $-7e^{8} + 79e^{6} - 257e^{4} + 194e^{2} - 30$ |
| 89 | $[89, 89, 2w^{2} + 2w - 19]$ | $\phantom{-}10e^{9} - 117e^{7} + 404e^{5} - 365e^{3} + 87e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} - w + 11]$ | $1$ |