Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,8,-443w + 4915]$ |
| Dimension: | $37$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $79$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{37} - x^{36} - 55x^{35} + 56x^{34} + 1381x^{33} - 1433x^{32} - 20979x^{31} + 22200x^{30} + 215420x^{29} - 232580x^{28} - 1582285x^{27} + 1743564x^{26} + 8580601x^{25} - 9653135x^{24} - 34956314x^{23} + 40162748x^{22} + 107810034x^{21} - 126562956x^{20} - 251739893x^{19} + 302151719x^{18} + 441955644x^{17} - 542757983x^{16} - 575014951x^{15} + 722940949x^{14} + 541764177x^{13} - 696769333x^{12} - 357393437x^{11} + 467468639x^{10} + 157837170x^{9} - 205170482x^{8} - 44519172x^{7} + 52942549x^{6} + 7924411x^{5} - 6484426x^{4} - 874200x^{3} + 195696x^{2} + 16371x + 289\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 10]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 11]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -116w - 1171]$ | $...$ |
| 5 | $[5, 5, 116w - 1287]$ | $...$ |
| 7 | $[7, 7, -1002w - 10115]$ | $...$ |
| 7 | $[7, 7, 1002w - 11117]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, 10w - 111]$ | $...$ |
| 11 | $[11, 11, -10w - 101]$ | $...$ |
| 23 | $[23, 23, -32w + 355]$ | $...$ |
| 23 | $[23, 23, 32w + 323]$ | $...$ |
| 41 | $[41, 41, -8w - 81]$ | $...$ |
| 41 | $[41, 41, -8w + 89]$ | $...$ |
| 53 | $[53, 53, 4w - 45]$ | $...$ |
| 53 | $[53, 53, 4w + 41]$ | $...$ |
| 59 | $[59, 59, -3892w + 43181]$ | $...$ |
| 59 | $[59, 59, 3892w + 39289]$ | $...$ |
| 61 | $[61, 61, 770w - 8543]$ | $...$ |
| 61 | $[61, 61, -770w - 7773]$ | $...$ |
| 67 | $[67, 67, 158w + 1595]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 11]$ | $-1$ |