Base field \(\Q(\sqrt{101}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 25\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[25,25,-w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 9x^{2} - 27x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{2}e^{2} - \frac{7}{4}e - 3$ |
| 5 | $[5, 5, -w - 4]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 4e + 3$ |
| 13 | $[13, 13, w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 4e - 3$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{3}{4}e^{3} + e^{2} - \frac{31}{4}e - 7$ |
| 17 | $[17, 17, -w + 7]$ | $-\frac{3}{4}e^{3} - e^{2} + \frac{31}{4}e + 7$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}e^{2} - 7$ |
| 19 | $[19, 19, w - 3]$ | $\phantom{-}e^{2} - 7$ |
| 23 | $[23, 23, w + 1]$ | $-\frac{1}{2}e^{3} - e^{2} + \frac{13}{2}e + 9$ |
| 23 | $[23, 23, -w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{13}{2}e - 9$ |
| 31 | $[31, 31, -w - 7]$ | $-e + 1$ |
| 31 | $[31, 31, w - 8]$ | $-e + 1$ |
| 37 | $[37, 37, 2w - 9]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{4}e - 4$ |
| 37 | $[37, 37, 2w + 7]$ | $-\frac{1}{4}e^{3} + \frac{13}{4}e + 4$ |
| 43 | $[43, 43, 4w + 17]$ | $-2e - 4$ |
| 43 | $[43, 43, 4w - 21]$ | $\phantom{-}2e + 4$ |
| 47 | $[47, 47, -w - 8]$ | $\phantom{-}e^{3} + e^{2} - 9e - 11$ |
| 47 | $[47, 47, w - 9]$ | $-e^{3} - e^{2} + 9e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,w + 4]$ | $1$ |