Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 4x^{6} - 8x^{5} + 40x^{4} + 10x^{3} - 108x^{2} + 16x + 72\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}e^{2} - e - 4$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ | $-2e^{6} + 5e^{5} + 23e^{4} - 44e^{3} - 83e^{2} + 81e + 90$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{9}{4}e^{6} + 5e^{5} + 28e^{4} - 45e^{3} - \frac{217}{2}e^{2} + 86e + 118$ |
| 29 | $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ | $-\frac{7}{2}e^{6} + \frac{17}{2}e^{5} + 41e^{4} - 75e^{3} - 150e^{2} + 141e + 156$ |
| 32 | $[32, 2, 2]$ | $-\frac{1}{2}e^{6} + \frac{3}{2}e^{5} + 6e^{4} - 14e^{3} - 25e^{2} + 29e + 33$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - 7e^{4} + 10e^{3} + 29e^{2} - 20e - 28$ |
| 41 | $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ | $\phantom{-}1$ |
| 43 | $[43, 43, -2w^{4} + 3w^{3} + 8w^{2} - 8w - 6]$ | $-\frac{1}{4}e^{6} + e^{5} + 2e^{4} - 8e^{3} - \frac{11}{2}e^{2} + 13e + 10$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 5w^{2} + 6w + 5]$ | $-\frac{3}{2}e^{6} + \frac{7}{2}e^{5} + 17e^{4} - 29e^{3} - 61e^{2} + 49e + 68$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ | $\phantom{-}\frac{11}{4}e^{6} - 7e^{5} - 32e^{4} + 63e^{3} + \frac{233}{2}e^{2} - 122e - 122$ |
| 61 | $[61, 61, w^{2} - 2w - 3]$ | $\phantom{-}\frac{5}{2}e^{6} - \frac{13}{2}e^{5} - 29e^{4} + 58e^{3} + 105e^{2} - 109e - 108$ |
| 67 | $[67, 67, w^{4} - w^{3} - 4w^{2} + 3w]$ | $\phantom{-}\frac{9}{2}e^{6} - 11e^{5} - 53e^{4} + 97e^{3} + 196e^{2} - 178e - 208$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $\phantom{-}\frac{13}{4}e^{6} - 8e^{5} - 39e^{4} + 71e^{3} + \frac{301}{2}e^{2} - 133e - 166$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 5]$ | $-\frac{9}{4}e^{6} + 6e^{5} + 25e^{4} - 52e^{3} - \frac{179}{2}e^{2} + 92e + 102$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 5w + 3]$ | $-e^{6} + \frac{5}{2}e^{5} + 11e^{4} - 21e^{3} - 35e^{2} + 35e + 26$ |
| 71 | $[71, 71, 2w^{4} - 2w^{3} - 8w^{2} + 5w + 4]$ | $\phantom{-}3e^{6} - \frac{15}{2}e^{5} - 35e^{4} + 67e^{3} + 127e^{2} - 125e - 134$ |
| 73 | $[73, 73, -2w^{4} + 2w^{3} + 9w^{2} - 5w - 6]$ | $\phantom{-}\frac{3}{2}e^{6} - 4e^{5} - 17e^{4} + 35e^{3} + 61e^{2} - 65e - 66$ |
| 81 | $[81, 3, -2w^{4} + 3w^{3} + 10w^{2} - 9w - 10]$ | $-\frac{3}{2}e^{6} + 4e^{5} + 16e^{4} - 34e^{3} - 52e^{2} + 60e + 52$ |
| 97 | $[97, 97, -2w^{4} + 3w^{3} + 7w^{2} - 5w - 4]$ | $-\frac{9}{4}e^{6} + 6e^{5} + 27e^{4} - 56e^{3} - \frac{207}{2}e^{2} + 115e + 112$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ | $-1$ |