Base field 4.4.8957.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ |
| Dimension: | $7$ |
| 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:
| \(x^{7} - 3x^{6} - 11x^{5} + 35x^{4} + 8x^{3} - 51x^{2} + 28x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + w^{2} + 5w]$ | $-\frac{3}{2}e^{6} + \frac{7}{2}e^{5} + \frac{37}{2}e^{4} - \frac{81}{2}e^{3} - 35e^{2} + \frac{111}{2}e - 12$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-e^{6} + 3e^{5} + 12e^{4} - 35e^{3} - 19e^{2} + 53e - 14$ |
| 13 | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $-1$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ | $-e^{4} - e^{3} + 10e^{2} + 8e - 5$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{3}{2}e^{6} - \frac{7}{2}e^{5} - \frac{37}{2}e^{4} + \frac{81}{2}e^{3} + 35e^{2} - \frac{111}{2}e + 12$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}e^{6} - 3e^{5} - 12e^{4} + 34e^{3} + 19e^{2} - 43e + 16$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}2e^{6} - 4e^{5} - 25e^{4} + 46e^{3} + 52e^{2} - 59e + 6$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}2e^{6} - 5e^{5} - 26e^{4} + 57e^{3} + 60e^{2} - 74e + 8$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ | $-\frac{9}{2}e^{6} + \frac{23}{2}e^{5} + \frac{109}{2}e^{4} - \frac{267}{2}e^{3} - 93e^{2} + \frac{375}{2}e - 50$ |
| 53 | $[53, 53, w^{3} - 3w^{2} + 3]$ | $-4e^{6} + 11e^{5} + 48e^{4} - 127e^{3} - 78e^{2} + 178e - 46$ |
| 53 | $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ | $\phantom{-}3e^{6} - 8e^{5} - 37e^{4} + 91e^{3} + 68e^{2} - 115e + 28$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}3e^{6} - 8e^{5} - 36e^{4} + 93e^{3} + 59e^{2} - 135e + 36$ |
| 61 | $[61, 61, -w - 3]$ | $\phantom{-}2e^{6} - 6e^{5} - 25e^{4} + 70e^{3} + 48e^{2} - 105e + 20$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 4]$ | $-4e^{6} + 11e^{5} + 50e^{4} - 125e^{3} - 98e^{2} + 160e - 34$ |
| 79 | $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ | $-4e^{6} + 10e^{5} + 48e^{4} - 116e^{3} - 79e^{2} + 162e - 40$ |
| 79 | $[79, 79, w^{2} - 5]$ | $\phantom{-}e^{6} - 2e^{5} - 12e^{4} + 23e^{3} + 21e^{2} - 31e + 1$ |
| 101 | $[101, 101, w^{3} - 6w]$ | $-\frac{5}{2}e^{6} + \frac{9}{2}e^{5} + \frac{65}{2}e^{4} - \frac{103}{2}e^{3} - 79e^{2} + \frac{121}{2}e + 10$ |
| 101 | $[101, 101, w^{2} - 2w - 4]$ | $-2e^{6} + 5e^{5} + 23e^{4} - 60e^{3} - 28e^{2} + 98e - 36$ |
| 103 | $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ | $\phantom{-}e^{6} - 4e^{5} - 12e^{4} + 45e^{3} + 17e^{2} - 57e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $1$ |