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: | $[14, 14, 3w + 14]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 6x^{2} + 12x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $-1$ |
| 2 | $[2, 2, w + 5]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 6w - 35]$ | $-1$ |
| 7 | $[7, 7, -6w - 29]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e - \frac{5}{2}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{3} - 5e$ |
| 11 | $[11, 11, 4w + 19]$ | $\phantom{-}e^{2} - 3$ |
| 11 | $[11, 11, 4w - 23]$ | $-\frac{3}{2}e^{3} + \frac{3}{2}e^{2} + \frac{17}{2}e - \frac{13}{2}$ |
| 13 | $[13, 13, -2w + 11]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{5}{2}$ |
| 13 | $[13, 13, 2w + 9]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e + \frac{1}{2}$ |
| 25 | $[25, 5, -5]$ | $-\frac{5}{2}e^{3} + \frac{1}{2}e^{2} + \frac{31}{2}e - \frac{11}{2}$ |
| 31 | $[31, 31, 2w - 13]$ | $\phantom{-}e^{2} - 2e - 1$ |
| 31 | $[31, 31, -2w - 11]$ | $\phantom{-}e^{2} - 2e - 7$ |
| 41 | $[41, 41, -8w - 39]$ | $-3e^{3} + 2e^{2} + 17e - 10$ |
| 41 | $[41, 41, 8w - 47]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{5}{2}e - \frac{19}{2}$ |
| 53 | $[53, 53, -26w - 125]$ | $-\frac{7}{2}e^{3} + \frac{1}{2}e^{2} + \frac{39}{2}e - \frac{9}{2}$ |
| 53 | $[53, 53, 26w - 151]$ | $\phantom{-}2e^{3} - 10e + 2$ |
| 61 | $[61, 61, -14w + 81]$ | $-\frac{5}{2}e^{3} + \frac{5}{2}e^{2} + \frac{27}{2}e - \frac{11}{2}$ |
| 61 | $[61, 61, -14w - 67]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{5}{2}e^{2} - \frac{31}{2}e + \frac{31}{2}$ |
| 83 | $[83, 83, 2w - 15]$ | $\phantom{-}2e^{3} - 2e^{2} - 6e + 10$ |
| 83 | $[83, 83, -2w - 13]$ | $-2e^{3} + 10e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 6]$ | $1$ |
| $7$ | $[7, 7, 6w - 35]$ | $1$ |