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: | $[8, 8, -w - 9]$ |
| Dimension: | $28$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{28} + 2x^{27} - 37x^{26} - 72x^{25} + 604x^{24} + 1144x^{23} - 5727x^{22} - 10548x^{21} + 34978x^{20} + 62406x^{19} - 144485x^{18} - 247362x^{17} + 413672x^{16} + 666220x^{15} - 831728x^{14} - 1212440x^{13} + 1184144x^{12} + 1456420x^{11} - 1195881x^{10} - 1100600x^{9} + 836759x^{8} + 470644x^{7} - 373418x^{6} - 83034x^{5} + 86110x^{4} - 3136x^{3} - 5004x^{2} + 380x + 44\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 160]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -17w + 177]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -842w + 8767]$ | $...$ |
| 7 | $[7, 7, -2w + 21]$ | $...$ |
| 7 | $[7, 7, 2w + 19]$ | $...$ |
| 13 | $[13, 13, -12w - 113]$ | $...$ |
| 13 | $[13, 13, 12w - 125]$ | $...$ |
| 17 | $[17, 17, 182w - 1895]$ | $...$ |
| 17 | $[17, 17, 182w + 1713]$ | $...$ |
| 23 | $[23, 23, -512w - 4819]$ | $...$ |
| 23 | $[23, 23, 512w - 5331]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 29 | $[29, 29, 22w - 229]$ | $...$ |
| 29 | $[29, 29, 22w + 207]$ | $...$ |
| 43 | $[43, 43, 114w + 1073]$ | $...$ |
| 43 | $[43, 43, 114w - 1187]$ | $...$ |
| 47 | $[47, 47, 8w - 83]$ | $...$ |
| 47 | $[47, 47, -8w - 75]$ | $...$ |
| 61 | $[61, 61, -1172w - 11031]$ | $...$ |
| 61 | $[61, 61, 1172w - 12203]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -17w + 177]$ | $-1$ |