Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + 11]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 11x^{4} + 14x^{3} + 37x^{2} - 12x - 28\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $-\frac{1}{4}e^{5} + e^{4} + \frac{7}{4}e^{3} - 7e^{2} - \frac{13}{4}e + \frac{11}{2}$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $\phantom{-}e^{2} - e - 4$ |
| 7 | $[7, 7, -w^{2} + 11]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{2} + 9]$ | $-\frac{1}{4}e^{5} + e^{4} + \frac{7}{4}e^{3} - 7e^{2} - \frac{9}{4}e + \frac{11}{2}$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{2}e^{5} + e^{4} + \frac{9}{2}e^{3} - 7e^{2} - \frac{17}{2}e + 8$ |
| 13 | $[13, 13, -w]$ | $\phantom{-}e^{5} - 3e^{4} - 7e^{3} + 21e^{2} + 8e - 24$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{1}{4}e^{5} + e^{4} + \frac{3}{4}e^{3} - 6e^{2} + \frac{7}{4}e + \frac{7}{2}$ |
| 23 | $[23, 23, w^{2} + w - 10]$ | $-\frac{1}{2}e^{5} + 3e^{4} + \frac{5}{2}e^{3} - 23e^{2} - \frac{3}{2}e + 28$ |
| 29 | $[29, 29, 2w^{2} - 21]$ | $-\frac{1}{2}e^{5} + e^{4} + \frac{7}{2}e^{3} - 5e^{2} - \frac{11}{2}e + 3$ |
| 37 | $[37, 37, 2w^{2} + w - 17]$ | $-\frac{3}{4}e^{5} + 2e^{4} + \frac{21}{4}e^{3} - 13e^{2} - \frac{27}{4}e + \frac{41}{2}$ |
| 43 | $[43, 43, 3w^{2} + 3w - 22]$ | $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} + 2e^{2} + \frac{3}{2}e - 5$ |
| 47 | $[47, 47, w^{2} - 6]$ | $\phantom{-}e^{5} - 4e^{4} - 7e^{3} + 31e^{2} + 10e - 40$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{9}{4}e^{5} + 7e^{4} + \frac{67}{4}e^{3} - 49e^{2} - \frac{109}{4}e + \frac{95}{2}$ |
| 47 | $[47, 47, -w^{2} + 12]$ | $-e^{5} + 2e^{4} + 8e^{3} - 14e^{2} - 12e + 21$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-e^{5} + 3e^{4} + 7e^{3} - 19e^{2} - 9e + 18$ |
| 61 | $[61, 61, w^{2} - 5]$ | $-\frac{3}{4}e^{5} + 2e^{4} + \frac{21}{4}e^{3} - 15e^{2} - \frac{19}{4}e + \frac{45}{2}$ |
| 67 | $[67, 67, w^{2} - w - 7]$ | $-\frac{3}{2}e^{5} + 4e^{4} + \frac{25}{2}e^{3} - 28e^{2} - \frac{49}{2}e + 27$ |
| 73 | $[73, 73, 7w^{2} + 3w - 66]$ | $-e^{5} + 4e^{4} + 8e^{3} - 29e^{2} - 16e + 21$ |
| 79 | $[79, 79, 2w^{2} - 19]$ | $\phantom{-}\frac{5}{2}e^{5} - 7e^{4} - \frac{37}{2}e^{3} + 49e^{2} + \frac{55}{2}e - 53$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + 11]$ | $-1$ |