Base field 6.6.1292517.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 6x^{2} - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[53, 53, -w^{5} - w^{4} + 6w^{3} + 5w^{2} - 4w - 1]$ |
| Dimension: | $23$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{23} - 6x^{22} - 97x^{21} + 641x^{20} + 3581x^{19} - 27489x^{18} - 62886x^{17} + 624154x^{16} + 502234x^{15} - 8400172x^{14} - 265956x^{13} + 71006332x^{12} - 27812333x^{11} - 388567660x^{10} + 237844488x^{9} + 1390347264x^{8} - 966055824x^{7} - 3216486016x^{6} + 2148580928x^{5} + 4615261952x^{4} - 2499312384x^{3} - 3712464896x^{2} + 1180247040x + 1265741824\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{5} + 6w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 5w + 1]$ | $...$ |
| 17 | $[17, 17, w^{5} - 5w^{3} - 2w^{2} + w + 2]$ | $...$ |
| 17 | $[17, 17, w^{4} - 5w^{2} - 2w + 1]$ | $...$ |
| 17 | $[17, 17, -w^{5} - w^{4} + 5w^{3} + 7w^{2} - 3]$ | $...$ |
| 19 | $[19, 19, 2w^{5} - 11w^{3} - 2w^{2} + 7w]$ | $...$ |
| 19 | $[19, 19, w^{5} - 5w^{3} - w^{2} + 2w - 1]$ | $...$ |
| 37 | $[37, 37, w^{5} - 5w^{3} - 2w^{2} + 2w + 3]$ | $...$ |
| 37 | $[37, 37, -2w^{5} - w^{4} + 11w^{3} + 8w^{2} - 6w - 2]$ | $...$ |
| 53 | $[53, 53, -w^{5} - w^{4} + 6w^{3} + 5w^{2} - 4w - 1]$ | $-1$ |
| 53 | $[53, 53, w^{3} - 4w + 1]$ | $...$ |
| 64 | $[64, 2, -2]$ | $...$ |
| 73 | $[73, 73, -3w^{5} + 17w^{3} + 3w^{2} - 12w + 1]$ | $...$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 1]$ | $...$ |
| 73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 7w^{2} + 5w + 3]$ | $...$ |
| 73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 8w^{2} + 5w + 4]$ | $...$ |
| 107 | $[107, 107, -w^{4} + w^{3} + 5w^{2} - 2w - 3]$ | $...$ |
| 107 | $[107, 107, -3w^{5} - w^{4} + 17w^{3} + 8w^{2} - 11w - 2]$ | $...$ |
| 109 | $[109, 109, w^{4} - 6w^{2} + 5]$ | $...$ |
| 109 | $[109, 109, -w^{5} + 6w^{3} + w^{2} - 7w + 1]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53, 53, -w^{5} - w^{4} + 6w^{3} + 5w^{2} - 4w - 1]$ | $1$ |