Base field \(\Q(\sqrt{393}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 98\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 14x^{4} + 59x^{2} - 74\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 160]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -17w + 177]$ | $-e$ |
| 3 | $[3, 3, -842w + 8767]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 8$ |
| 7 | $[7, 7, -2w + 21]$ | $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} - 12$ |
| 7 | $[7, 7, 2w + 19]$ | $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} - 12$ |
| 13 | $[13, 13, -12w - 113]$ | $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 16$ |
| 13 | $[13, 13, 12w - 125]$ | $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 16$ |
| 17 | $[17, 17, 182w - 1895]$ | $-e^{3} + 5e$ |
| 17 | $[17, 17, 182w + 1713]$ | $\phantom{-}e^{3} - 5e$ |
| 23 | $[23, 23, -512w - 4819]$ | $\phantom{-}e^{5} - 10e^{3} + 21e$ |
| 23 | $[23, 23, 512w - 5331]$ | $-e^{5} + 10e^{3} - 21e$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} - 3$ |
| 29 | $[29, 29, 22w - 229]$ | $\phantom{-}e^{5} - 11e^{3} + 26e$ |
| 29 | $[29, 29, 22w + 207]$ | $-e^{5} + 11e^{3} - 26e$ |
| 43 | $[43, 43, 114w + 1073]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 2$ |
| 43 | $[43, 43, 114w - 1187]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 2$ |
| 47 | $[47, 47, 8w - 83]$ | $\phantom{-}e^{3} - 7e$ |
| 47 | $[47, 47, -8w - 75]$ | $-e^{3} + 7e$ |
| 61 | $[61, 61, -1172w - 11031]$ | $-\frac{3}{2}e^{4} + \frac{29}{2}e^{2} - 22$ |
| 61 | $[61, 61, 1172w - 12203]$ | $-\frac{3}{2}e^{4} + \frac{29}{2}e^{2} - 22$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).