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: | $[16,8,10w - 58]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 4x^{2} - 16x - 56\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $-1$ |
| 2 | $[2, 2, w + 5]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 6w - 35]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -6w - 29]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{2} - e + 6$ |
| 11 | $[11, 11, 4w + 19]$ | $-\frac{1}{2}e^{2} + 10$ |
| 11 | $[11, 11, 4w - 23]$ | $\phantom{-}\frac{1}{2}e^{2} + e - 6$ |
| 13 | $[13, 13, -2w + 11]$ | $-\frac{1}{2}e^{2} - e + 6$ |
| 13 | $[13, 13, 2w + 9]$ | $\phantom{-}\frac{1}{2}e^{2} - 10$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{2}e^{2} - e - 12$ |
| 31 | $[31, 31, 2w - 13]$ | $-e$ |
| 31 | $[31, 31, -2w - 11]$ | $\phantom{-}e^{2} - 16$ |
| 41 | $[41, 41, -8w - 39]$ | $\phantom{-}e - 4$ |
| 41 | $[41, 41, 8w - 47]$ | $-e - 4$ |
| 53 | $[53, 53, -26w - 125]$ | $\phantom{-}\frac{1}{2}e^{2} + e - 6$ |
| 53 | $[53, 53, 26w - 151]$ | $\phantom{-}\frac{1}{2}e^{2} - 18$ |
| 61 | $[61, 61, -14w + 81]$ | $-6$ |
| 61 | $[61, 61, -14w - 67]$ | $\phantom{-}e^{2} + 2e - 10$ |
| 83 | $[83, 83, 2w - 15]$ | $-\frac{1}{2}e^{2} - e + 6$ |
| 83 | $[83, 83, -2w - 13]$ | $-\frac{1}{2}e^{2} - 2e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,w + 5]$ | $-1$ |
| $2$ | $[2,2,-w + 6]$ | $1$ |