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: | $[7, 7, 186w - 1385]$ |
| Dimension: | $31$ |
| 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:
| \(x^{31} - 7x^{30} - 25x^{29} + 271x^{28} + 112x^{27} - 4614x^{26} + 3190x^{25} + 45428x^{24} - 59388x^{23} - 285773x^{22} + 504205x^{21} + 1194646x^{20} - 2634307x^{19} - 3322093x^{18} + 9195446x^{17} + 5848234x^{16} - 22070286x^{15} - 5257877x^{14} + 36536588x^{13} - 1354258x^{12} - 41003654x^{11} + 9963616x^{10} + 29862934x^{9} - 12366323x^{8} - 12821905x^{7} + 7565144x^{6} + 2477377x^{5} - 2266219x^{4} + 67129x^{3} + 235823x^{2} - 57437x + 4014\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -9w - 58]$ | $...$ |
| 2 | $[2, 2, -9w + 67]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w + 15]$ | $...$ |
| 3 | $[3, 3, 2w + 13]$ | $...$ |
| 7 | $[7, 7, 186w - 1385]$ | $-1$ |
| 7 | $[7, 7, -186w - 1199]$ | $...$ |
| 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 |
|---|---|---|
| $7$ | $[7, 7, 186w - 1385]$ | $1$ |