Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[35, 35, w^{2} - w - 2]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} - 12x^{14} + 17x^{13} + 308x^{12} - 1179x^{11} - 1799x^{10} + 14381x^{9} - 6831x^{8} - 62203x^{7} + 77403x^{6} + 92727x^{5} - 173230x^{4} - 30416x^{3} + 127584x^{2} - 16960x - 17280\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-1$ |
| 7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $...$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $...$ |
| 32 | $[32, 2, 2]$ | $...$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $...$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $...$ |
| 43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $...$ |
| 43 | $[43, 43, -w^{2} + w + 3]$ | $...$ |
| 47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $...$ |
| 61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $...$ |
| 79 | $[79, 79, w^{2} - w - 5]$ | $...$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $...$ |
| 79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $...$ |
| 97 | $[97, 97, w^{3} - 6w]$ | $...$ |
| 101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $...$ |
| 101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $...$ |
| 107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,w^{4}-w^{3}-5w^{2}+3w+1]$ | $1$ |
| $7$ | $[7,7,-w^{4}+2w^{3}+4w^{2}-6w]$ | $-1$ |