Base field 6.6.1081856.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 7x^{2} + 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, -w^{3} + 4w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 21x^{3} - 11x^{2} + 4x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ | $-\frac{1}{4}e^{4} + \frac{21}{4}e^{2} - \frac{5}{2}e - \frac{3}{2}$ |
| 17 | $[17, 17, -w^{2} + w + 2]$ | $-\frac{9}{4}e^{4} - \frac{3}{2}e^{3} + \frac{191}{4}e^{2} + \frac{17}{2}e - \frac{19}{2}$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ | $\phantom{-}\frac{5}{4}e^{4} + e^{3} - \frac{105}{4}e^{2} - \frac{19}{2}e + \frac{1}{2}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{15}{4}e^{4} + \frac{5}{2}e^{3} - \frac{317}{4}e^{2} - \frac{29}{2}e + \frac{25}{2}$ |
| 31 | $[31, 31, -w^{3} + 4w + 1]$ | $\phantom{-}1$ |
| 31 | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ | $\phantom{-}5e^{4} + \frac{5}{2}e^{3} - \frac{213}{2}e^{2} - 2e + 23$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ | $-\frac{19}{4}e^{4} - 3e^{3} + \frac{403}{4}e^{2} + \frac{27}{2}e - \frac{39}{2}$ |
| 47 | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ | $-\frac{21}{4}e^{4} - 3e^{3} + \frac{445}{4}e^{2} + \frac{19}{2}e - \frac{45}{2}$ |
| 49 | $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ | $\phantom{-}\frac{13}{4}e^{4} + \frac{3}{2}e^{3} - \frac{275}{4}e^{2} + \frac{1}{2}e + \frac{15}{2}$ |
| 71 | $[71, 71, -w^{4} + 5w^{2} + w - 3]$ | $\phantom{-}\frac{7}{4}e^{4} + \frac{1}{2}e^{3} - \frac{149}{4}e^{2} + \frac{11}{2}e + \frac{9}{2}$ |
| 71 | $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ | $\phantom{-}\frac{11}{4}e^{4} + 2e^{3} - \frac{231}{4}e^{2} - \frac{29}{2}e + \frac{15}{2}$ |
| 73 | $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ | $\phantom{-}\frac{17}{2}e^{4} + 4e^{3} - \frac{363}{2}e^{2} + e + 41$ |
| 73 | $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ | $-\frac{9}{4}e^{4} - e^{3} + \frac{193}{4}e^{2} - \frac{5}{2}e - \frac{29}{2}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $-6e^{4} - \frac{7}{2}e^{3} + \frac{255}{2}e^{2} + 14e - 31$ |
| 89 | $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ | $\phantom{-}3e^{4} + 2e^{3} - 64e^{2} - 13e + 18$ |
| 97 | $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ | $-\frac{3}{2}e^{4} - \frac{3}{2}e^{3} + 31e^{2} + 17e - 8$ |
| 103 | $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ | $-\frac{9}{4}e^{4} - \frac{5}{2}e^{3} + \frac{187}{4}e^{2} + \frac{59}{2}e - \frac{7}{2}$ |
| 103 | $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ | $-\frac{11}{4}e^{4} - \frac{3}{2}e^{3} + \frac{237}{4}e^{2} + \frac{5}{2}e - \frac{37}{2}$ |
| 103 | $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-\frac{7}{4}e^{4} + \frac{151}{4}e^{2} - \frac{39}{2}e - \frac{19}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, -w^{3} + 4w + 1]$ | $-1$ |