Base field 6.6.1683101.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49, 7, -w^{5} + 4w^{4} - w^{3} - 11w^{2} + 7w + 7]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 19x^{2} - 24x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{2}e^{2} - \frac{17}{4}e - \frac{7}{2}$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{17}{4}e + \frac{7}{2}$ |
| 29 | $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{23}{4}e + \frac{1}{2}$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{23}{4}e + \frac{1}{2}$ |
| 41 | $[41, 41, -w^{2} + 4]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{2}e^{2} - \frac{21}{4}e + \frac{11}{2}$ |
| 41 | $[41, 41, -w^{2} + 2w + 3]$ | $-\frac{1}{4}e^{3} + \frac{1}{2}e^{2} + \frac{21}{4}e - \frac{11}{2}$ |
| 43 | $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 8e + 2$ |
| 43 | $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 8e + 2$ |
| 64 | $[64, 2, -2]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}e + 14$ |
| 71 | $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
| 71 | $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ | $-\frac{1}{2}e^{3} + \frac{17}{2}e - 1$ |
| 83 | $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e + 1$ |
| 97 | $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $-\frac{1}{4}e^{3} - e^{2} + \frac{7}{4}e + \frac{13}{2}$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{4}e^{3} + e^{2} - \frac{7}{4}e - \frac{13}{2}$ |
| 113 | $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ | $-\frac{1}{4}e^{3} - \frac{1}{2}e^{2} + \frac{13}{4}e - \frac{15}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $-1$ |