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: | $[7,7,-186w - 1199]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} + 4x^{16} - 18x^{15} - 84x^{14} + 113x^{13} + 696x^{12} - 240x^{11} - 2902x^{10} - 322x^{9} + 6433x^{8} + 2238x^{7} - 7323x^{6} - 3483x^{5} + 3762x^{4} + 1976x^{3} - 650x^{2} - 254x + 61\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -9w - 58]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -9w + 67]$ | $...$ |
| 3 | $[3, 3, -2w + 15]$ | $...$ |
| 3 | $[3, 3, 2w + 13]$ | $...$ |
| 7 | $[7, 7, 186w - 1385]$ | $...$ |
| 7 | $[7, 7, -186w - 1199]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -38w - 245]$ | $...$ |
| 23 | $[23, 23, 38w - 283]$ | $...$ |
| 25 | $[25, 5, 5]$ | $...$ |
| 31 | $[31, 31, 16w - 119]$ | $...$ |
| 31 | $[31, 31, 16w + 103]$ | $...$ |
| 43 | $[43, 43, 4w + 25]$ | $...$ |
| 43 | $[43, 43, -4w + 29]$ | $...$ |
| 59 | $[59, 59, 12w - 89]$ | $...$ |
| 59 | $[59, 59, -12w - 77]$ | $...$ |
| 67 | $[67, 67, 92w + 593]$ | $...$ |
| 67 | $[67, 67, 92w - 685]$ | $...$ |
| 83 | $[83, 83, 204w - 1519]$ | $...$ |
| 83 | $[83, 83, 204w + 1315]$ | $...$ |
| 97 | $[97, 97, -24w + 179]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-186w - 1199]$ | $-1$ |