Base field \(\Q(\sqrt{193}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 48\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6,6,w - 7]$ |
| 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:
| \(x^{4} + 3x^{3} - 3x^{2} - 12x - 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -9w - 58]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -9w + 67]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -2w + 15]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 7$ |
| 3 | $[3, 3, 2w + 13]$ | $-1$ |
| 7 | $[7, 7, 186w - 1385]$ | $-e^{3} - 2e^{2} + 4e + 6$ |
| 7 | $[7, 7, -186w - 1199]$ | $-e^{3} - e^{2} + 5e + 3$ |
| 23 | $[23, 23, -38w - 245]$ | $-e^{2}$ |
| 23 | $[23, 23, 38w - 283]$ | $-2e^{2} + 9$ |
| 25 | $[25, 5, 5]$ | $-e^{2} + 3$ |
| 31 | $[31, 31, 16w - 119]$ | $\phantom{-}e^{3} + 2e^{2} - 4e - 9$ |
| 31 | $[31, 31, 16w + 103]$ | $\phantom{-}4e^{3} + 7e^{2} - 19e - 24$ |
| 43 | $[43, 43, 4w + 25]$ | $-2e^{3} - 3e^{2} + 9e + 9$ |
| 43 | $[43, 43, -4w + 29]$ | $\phantom{-}e^{3} + 2e^{2} - 6e - 12$ |
| 59 | $[59, 59, 12w - 89]$ | $-e^{3} + 5e - 6$ |
| 59 | $[59, 59, -12w - 77]$ | $\phantom{-}5e^{3} + 9e^{2} - 24e - 27$ |
| 67 | $[67, 67, 92w + 593]$ | $-3e^{3} - 6e^{2} + 12e + 25$ |
| 67 | $[67, 67, 92w - 685]$ | $\phantom{-}2e^{3} + 4e^{2} - 9e - 20$ |
| 83 | $[83, 83, 204w - 1519]$ | $-e^{3} - 2e^{2} + 6$ |
| 83 | $[83, 83, 204w + 1315]$ | $\phantom{-}e^{3} + 3e^{2} - e - 12$ |
| 97 | $[97, 97, -24w + 179]$ | $\phantom{-}3e^{3} + 8e^{2} - 12e - 30$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,9w - 67]$ | $-1$ |
| $3$ | $[3,3,2w + 13]$ | $1$ |