Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $135$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} + 16x^{2} + 64x + 256\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1}{64}e^{3} + \frac{1}{16}e^{2} + \frac{1}{4}e + 1$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{4}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{1}{16}e^{3} - \frac{1}{4}e^{2} - e - 4$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{1}{4}e^{2}$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{1}{16}e^{3}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}2$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}\frac{3}{16}e^{2}$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}\frac{3}{64}e^{3}$ |
| 29 | $[29, 29, w + 6]$ | $\phantom{-}2e$ |
| 29 | $[29, 29, w + 22]$ | $-\frac{1}{8}e^{3} - \frac{1}{2}e^{2} - 2e - 8$ |
| 41 | $[41, 41, w + 13]$ | $\phantom{-}\frac{5}{64}e^{3} + \frac{5}{16}e^{2} + \frac{5}{4}e + 5$ |
| 41 | $[41, 41, w + 27]$ | $-\frac{5}{4}e$ |
| 43 | $[43, 43, w + 16]$ | $-\frac{9}{16}e^{2}$ |
| 43 | $[43, 43, w + 26]$ | $-\frac{9}{64}e^{3}$ |
| 47 | $[47, 47, w + 2]$ | $\phantom{-}\frac{3}{2}e$ |
| 47 | $[47, 47, w + 44]$ | $-\frac{3}{32}e^{3} - \frac{3}{8}e^{2} - \frac{3}{2}e - 6$ |
| 73 | $[73, 73, w + 33]$ | $\phantom{-}\frac{1}{4}e$ |
| 73 | $[73, 73, w + 39]$ | $-\frac{1}{64}e^{3} - \frac{1}{16}e^{2} - \frac{1}{4}e - 1$ |
| 83 | $[83, 83, -4w - 37]$ | $\phantom{-}7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{1}{64}e^{3} - \frac{1}{16}e^{2} - \frac{1}{4}e - 1$ |
| $2$ | $[2, 2, w + 1]$ | $\frac{1}{4}e$ |