Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,8,w + 4]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - x^{5} - 10x^{4} + 7x^{3} + 22x^{2} - 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 6w - 35]$ | $-e^{5} + e^{4} + 9e^{3} - 7e^{2} - 16e + 2$ |
| 7 | $[7, 7, -6w - 29]$ | $-\frac{1}{2}e^{5} + 5e^{3} + \frac{1}{2}e^{2} - \frac{21}{2}e - \frac{5}{2}$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{5} + e^{4} + 5e^{3} - \frac{13}{2}e^{2} - \frac{23}{2}e + \frac{1}{2}$ |
| 11 | $[11, 11, 4w + 19]$ | $\phantom{-}\frac{1}{2}e^{5} - e^{4} - 5e^{3} + \frac{13}{2}e^{2} + \frac{21}{2}e + \frac{1}{2}$ |
| 11 | $[11, 11, 4w - 23]$ | $\phantom{-}e^{3} + e^{2} - 7e - 3$ |
| 13 | $[13, 13, -2w + 11]$ | $-\frac{1}{2}e^{5} + 4e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e - \frac{7}{2}$ |
| 13 | $[13, 13, 2w + 9]$ | $-e^{5} + e^{4} + 10e^{3} - 7e^{2} - 22e + 3$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}e^{3} - 5e - 2$ |
| 31 | $[31, 31, 2w - 13]$ | $\phantom{-}\frac{3}{2}e^{5} - 14e^{3} + \frac{1}{2}e^{2} + \frac{53}{2}e + \frac{3}{2}$ |
| 31 | $[31, 31, -2w - 11]$ | $-e^{5} + e^{4} + 10e^{3} - 7e^{2} - 23e$ |
| 41 | $[41, 41, -8w - 39]$ | $-2e^{2} + e + 9$ |
| 41 | $[41, 41, 8w - 47]$ | $-e^{5} + 2e^{4} + 12e^{3} - 13e^{2} - 34e + 2$ |
| 53 | $[53, 53, -26w - 125]$ | $\phantom{-}\frac{3}{2}e^{5} - e^{4} - 14e^{3} + \frac{17}{2}e^{2} + \frac{47}{2}e - \frac{13}{2}$ |
| 53 | $[53, 53, 26w - 151]$ | $-e^{5} + 8e^{3} - e^{2} - 12e + 6$ |
| 61 | $[61, 61, -14w + 81]$ | $\phantom{-}e^{5} - 10e^{3} + 25e + 2$ |
| 61 | $[61, 61, -14w - 67]$ | $-e^{5} + 10e^{3} + 2e^{2} - 25e - 8$ |
| 83 | $[83, 83, 2w - 15]$ | $-e^{5} + e^{4} + 8e^{3} - 6e^{2} - 9e + 7$ |
| 83 | $[83, 83, -2w - 13]$ | $-\frac{3}{2}e^{5} + 14e^{3} - \frac{3}{2}e^{2} - \frac{53}{2}e + \frac{7}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 6]$ | $1$ |