Base field \(\Q(\sqrt{29}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[53,53,-3w - 2]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 5x^{4} + x^{3} + 26x^{2} - 37x + 13\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-e^{4} + 3e^{3} + 4e^{2} - 16e + 11$ |
| 5 | $[5, 5, w - 2]$ | $\phantom{-}e^{4} - 3e^{3} - 5e^{2} + 17e - 6$ |
| 7 | $[7, 7, w]$ | $\phantom{-}5e^{4} - 11e^{3} - 26e^{2} + 58e - 23$ |
| 7 | $[7, 7, -w + 1]$ | $-2e^{4} + 3e^{3} + 12e^{2} - 13e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}4e^{4} - 9e^{3} - 21e^{2} + 48e - 18$ |
| 13 | $[13, 13, w + 4]$ | $-4e^{4} + 10e^{3} + 19e^{2} - 54e + 24$ |
| 13 | $[13, 13, w - 5]$ | $-4e^{4} + 12e^{3} + 17e^{2} - 66e + 37$ |
| 23 | $[23, 23, -w - 5]$ | $\phantom{-}3e^{4} - 8e^{3} - 13e^{2} + 44e - 26$ |
| 23 | $[23, 23, w - 6]$ | $-7e^{4} + 16e^{3} + 36e^{2} - 85e + 34$ |
| 29 | $[29, 29, 2w - 1]$ | $-8e^{4} + 20e^{3} + 40e^{2} - 108e + 45$ |
| 53 | $[53, 53, 3w - 5]$ | $\phantom{-}3e^{4} - 9e^{3} - 12e^{2} + 49e - 29$ |
| 53 | $[53, 53, -3w - 2]$ | $-1$ |
| 59 | $[59, 59, -3w - 1]$ | $\phantom{-}6e^{4} - 16e^{3} - 28e^{2} + 89e - 40$ |
| 59 | $[59, 59, 3w - 4]$ | $-3e^{4} + 7e^{3} + 14e^{2} - 37e + 22$ |
| 67 | $[67, 67, 3w - 13]$ | $-6e^{4} + 7e^{3} + 39e^{2} - 30e - 6$ |
| 67 | $[67, 67, -3w - 10]$ | $\phantom{-}7e^{4} - 17e^{3} - 34e^{2} + 89e - 40$ |
| 71 | $[71, 71, 2w - 11]$ | $\phantom{-}13e^{4} - 28e^{3} - 69e^{2} + 148e - 58$ |
| 71 | $[71, 71, -2w - 9]$ | $-9e^{4} + 21e^{3} + 45e^{2} - 111e + 45$ |
| 83 | $[83, 83, -w - 9]$ | $-11e^{4} + 20e^{3} + 61e^{2} - 97e + 26$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53,53,-3w - 2]$ | $1$ |