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: | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 19x^{4} + 12x^{3} + 91x^{2} - 112x + 19\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{1}{2}$ |
| 7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + \frac{7}{2}e^{3} + \frac{3}{2}e^{2} - \frac{45}{4}e + \frac{7}{4}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $\phantom{-}e + 3$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}e^{3} - 11e + 6$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{4} - 6e^{2} + e + \frac{15}{2}$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $-\frac{1}{2}e^{5} - e^{4} + \frac{15}{2}e^{3} + \frac{13}{2}e^{2} - 31e + \frac{35}{2}$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-\frac{1}{4}e^{5} - \frac{5}{4}e^{4} + \frac{5}{2}e^{3} + \frac{23}{2}e^{2} - \frac{33}{4}e - \frac{29}{4}$ |
| 43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $-\frac{1}{4}e^{5} - \frac{3}{4}e^{4} + \frac{7}{2}e^{3} + \frac{11}{2}e^{2} - \frac{61}{4}e + \frac{41}{4}$ |
| 43 | $[43, 43, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} + e^{4} - 7e^{3} - 7e^{2} + \frac{51}{2}e - 9$ |
| 47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $-e^{3} + e^{2} + 10e - 8$ |
| 61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 4e^{2} + 14e - \frac{15}{2}$ |
| 79 | $[79, 79, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{3}{4}e^{4} - \frac{9}{2}e^{3} - \frac{15}{2}e^{2} + \frac{85}{4}e + \frac{11}{4}$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}2e^{3} - 19e + 15$ |
| 79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $\phantom{-}e^{3} - 2e^{2} - 12e + 19$ |
| 97 | $[97, 97, w^{3} - 6w]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{9}{2}e^{2} + \frac{17}{2}e - 1$ |
| 101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $\phantom{-}\frac{3}{4}e^{5} + \frac{5}{4}e^{4} - 10e^{3} - 8e^{2} + \frac{137}{4}e - \frac{25}{4}$ |
| 101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $-\frac{1}{4}e^{5} + \frac{3}{4}e^{4} + \frac{11}{2}e^{3} - \frac{19}{2}e^{2} - \frac{109}{4}e + \frac{103}{4}$ |
| 107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $-\frac{3}{4}e^{5} - \frac{7}{4}e^{4} + \frac{21}{2}e^{3} + \frac{25}{2}e^{2} - \frac{167}{4}e + \frac{49}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,-w^{4}+2w^{3}+4w^{2}-6w]$ | $-1$ |