Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} - w + 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 15x^{10} + 82x^{8} - 203x^{6} + 220x^{4} - 76x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{1}{2}e^{11} + \frac{13}{2}e^{9} - 29e^{7} + \frac{111}{2}e^{5} - 45e^{3} + 13e$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $-\frac{1}{2}e^{11} + \frac{13}{2}e^{9} - 28e^{7} + \frac{91}{2}e^{5} - 18e^{3} - 7e$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}2e^{10} - 25e^{8} + 102e^{6} - 157e^{4} + 70e^{2} - 8$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{11} - \frac{11}{2}e^{9} + 17e^{7} - \frac{19}{2}e^{5} - 20e^{3} + 11e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}e^{11} - 13e^{9} + 57e^{7} - 102e^{5} + 71e^{3} - 20e$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $-2e^{10} + 25e^{8} - 101e^{6} + 148e^{4} - 51e^{2}$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $-e^{9} + 12e^{7} - 46e^{5} + 64e^{3} - 20e$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $-\frac{3}{2}e^{11} + \frac{39}{2}e^{9} - 85e^{7} + \frac{295}{2}e^{5} - 91e^{3} + 19e$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $\phantom{-}2e^{11} - 28e^{9} + 138e^{7} - 293e^{5} + 249e^{3} - 54e$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $-e^{11} + 12e^{9} - 43e^{7} + 37e^{5} + 39e^{3} - 24e$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $-2e^{10} + 26e^{8} - 115e^{6} + 211e^{4} - 146e^{2} + 20$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $-3e^{10} + 37e^{8} - 150e^{6} + 240e^{4} - 132e^{2} + 12$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $\phantom{-}\frac{5}{2}e^{11} - \frac{61}{2}e^{9} + 120e^{7} - \frac{349}{2}e^{5} + 60e^{3} + 19e$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $\phantom{-}3e^{11} - 38e^{9} + 158e^{7} - 248e^{5} + 108e^{3} - 2e$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $\phantom{-}e^{9} - 13e^{7} + 56e^{5} - 93e^{3} + 48e$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $-3e^{10} + 37e^{8} - 144e^{6} + 185e^{4} - 19e^{2} - 6$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}3e^{10} - 38e^{8} + 159e^{6} - 256e^{4} + 122e^{2} - 10$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $-\frac{3}{2}e^{11} + \frac{31}{2}e^{9} - 39e^{7} - \frac{33}{2}e^{5} + 116e^{3} - 41e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} - w + 3]$ | $-1$ |