Base field \(\Q(\sqrt{313}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 78\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 9x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3w + 28]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -3w - 25]$ | $\phantom{-}1$ |
| 3 | $[3, 3, 26w - 243]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -26w - 217]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -2w - 17]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 6$ |
| 11 | $[11, 11, -2w + 19]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 6$ |
| 13 | $[13, 13, 2148w + 17927]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e$ |
| 13 | $[13, 13, 2148w - 20075]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e$ |
| 19 | $[19, 19, -292w + 2729]$ | $-e^{2} + 4$ |
| 19 | $[19, 19, 292w + 2437]$ | $-e^{2} + 4$ |
| 25 | $[25, 5, -5]$ | $-e^{2} + 10$ |
| 29 | $[29, 29, 20w + 167]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 8$ |
| 29 | $[29, 29, 20w - 187]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 8$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{3}{2}e^{2} + \frac{3}{2}e - 4$ |
| 71 | $[71, 71, -240w + 2243]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e - 6$ |
| 71 | $[71, 71, 240w + 2003]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e - 6$ |
| 79 | $[79, 79, -3368w + 31477]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$ |
| 79 | $[79, 79, -3368w - 28109]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$ |
| 83 | $[83, 83, -84w - 701]$ | $\phantom{-}e^{2} + 4e - 12$ |
| 83 | $[83, 83, 84w - 785]$ | $\phantom{-}e^{2} + 4e - 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -3w + 28]$ | $-1$ |
| $2$ | $[2, 2, -3w - 25]$ | $-1$ |