Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} + 2w + 4]$ |
| 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:
| \(x^{6} - 28x^{4} + 248x^{2} - 688\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $-\frac{1}{4}e^{4} + \frac{11}{2}e^{2} - 27$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{2}e^{4} + \frac{19}{2}e^{2} - 41$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{4}e^{3} - 2e$ |
| 17 | $[17, 17, -w - 3]$ | $\phantom{-}\frac{3}{4}e^{4} - 14e^{2} + 62$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{19}{4}e^{3} + 21e$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{8}e^{5} + \frac{3}{2}e^{3} - e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 24$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}\frac{1}{4}e^{4} - 5e^{2} + 26$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + 13e$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} - 7e$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-\frac{3}{4}e^{3} + 7e$ |
| 37 | $[37, 37, 2w - 5]$ | $\phantom{-}\frac{1}{4}e^{5} - 5e^{3} + 22e$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $-\frac{1}{4}e^{4} + 4e^{2} - 18$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $-\frac{3}{4}e^{4} + 12e^{2} - 38$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $\phantom{-}\frac{3}{8}e^{5} - \frac{29}{4}e^{3} + 33e$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} - 4e^{2} + 16$ |
| 71 | $[71, 71, w - 5]$ | $-\frac{3}{4}e^{4} + 18e^{2} - 93$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.