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: | $5$ |
| 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:
| \(x^{5} + x^{4} - 12x^{3} + x^{2} + 19x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w + 1]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{4}{9}e^{4} - \frac{2}{3}e^{3} + \frac{14}{3}e^{2} + \frac{11}{9}e - \frac{14}{3}$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{2}{9}e^{4} + 3e^{2} - \frac{23}{9}e - \frac{13}{3}$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{2}{9}e^{4} - \frac{2}{3}e^{3} + \frac{5}{3}e^{2} + \frac{25}{9}e - \frac{7}{3}$ |
| 9 | $[9, 3, 3]$ | $-\frac{2}{9}e^{4} + 3e^{2} - \frac{23}{9}e - \frac{16}{3}$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}e^{2} + e - 6$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}\frac{2}{9}e^{4} + \frac{2}{3}e^{3} - \frac{5}{3}e^{2} - \frac{25}{9}e + \frac{4}{3}$ |
| 29 | $[29, 29, w + 6]$ | $-\frac{1}{3}e^{4} - \frac{4}{3}e^{3} + \frac{4}{3}e^{2} + \frac{19}{3}e + 2$ |
| 29 | $[29, 29, w + 22]$ | $\phantom{-}\frac{11}{9}e^{4} + 2e^{3} - 12e^{2} - \frac{31}{9}e + \frac{28}{3}$ |
| 41 | $[41, 41, w + 13]$ | $\phantom{-}\frac{2}{9}e^{4} + e^{3} - e^{2} - \frac{58}{9}e - \frac{8}{3}$ |
| 41 | $[41, 41, w + 27]$ | $\phantom{-}\frac{2}{9}e^{4} - \frac{1}{3}e^{3} - \frac{11}{3}e^{2} + \frac{38}{9}e + \frac{4}{3}$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{5}{3}e^{3} - \frac{20}{3}e^{2} - \frac{26}{3}e + 7$ |
| 43 | $[43, 43, w + 26]$ | $\phantom{-}\frac{2}{3}e^{4} + e^{3} - 6e^{2} + \frac{2}{3}e + 3$ |
| 47 | $[47, 47, w + 2]$ | $-\frac{2}{3}e^{4} - \frac{5}{3}e^{3} + \frac{14}{3}e^{2} + \frac{17}{3}e - 2$ |
| 47 | $[47, 47, w + 44]$ | $-\frac{4}{9}e^{4} - e^{3} + 4e^{2} + \frac{53}{9}e - \frac{2}{3}$ |
| 73 | $[73, 73, w + 33]$ | $\phantom{-}\frac{2}{9}e^{4} - \frac{1}{3}e^{3} - \frac{8}{3}e^{2} + \frac{20}{9}e - \frac{17}{3}$ |
| 73 | $[73, 73, w + 39]$ | $-\frac{2}{9}e^{4} - \frac{5}{3}e^{3} - \frac{4}{3}e^{2} + \frac{88}{9}e + \frac{11}{3}$ |
| 83 | $[83, 83, -4w - 37]$ | $\phantom{-}\frac{1}{9}e^{4} + \frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{44}{9}e - \frac{16}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $2$ | $[2, 2, w + 1]$ | $1$ |