Base field 4.4.11525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{12}{5}w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 32x^{2} - 41x + 63\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ | $-1$ |
| 5 | $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ | $\phantom{-}\frac{20}{293}e^{3} + \frac{84}{293}e^{2} - \frac{631}{293}e - \frac{1212}{293}$ |
| 16 | $[16, 2, 2]$ | $-\frac{18}{293}e^{3} - \frac{17}{293}e^{2} + \frac{480}{293}e - \frac{257}{293}$ |
| 19 | $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ | $-\frac{2}{293}e^{3} - \frac{67}{293}e^{2} - \frac{142}{293}e + \frac{883}{293}$ |
| 19 | $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ | $-\frac{10}{293}e^{3} - \frac{42}{293}e^{2} + \frac{169}{293}e - \frac{566}{293}$ |
| 19 | $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ | $-\frac{8}{293}e^{3} + \frac{25}{293}e^{2} + \frac{604}{293}e - \frac{863}{293}$ |
| 19 | $[19, 19, w - 1]$ | $-\frac{10}{293}e^{3} - \frac{42}{293}e^{2} + \frac{169}{293}e + \frac{1192}{293}$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}\frac{57}{293}e^{3} + \frac{5}{293}e^{2} - \frac{1813}{293}e - \frac{993}{293}$ |
| 29 | $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ | $-\frac{25}{293}e^{3} - \frac{105}{293}e^{2} + \frac{569}{293}e + \frac{1515}{293}$ |
| 31 | $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ | $-\frac{29}{293}e^{3} + \frac{54}{293}e^{2} + \frac{578}{293}e - \frac{1700}{293}$ |
| 31 | $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ | $\phantom{-}\frac{23}{293}e^{3} + \frac{38}{293}e^{2} - \frac{418}{293}e - \frac{632}{293}$ |
| 61 | $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ | $\phantom{-}\frac{2}{293}e^{3} + \frac{67}{293}e^{2} + \frac{142}{293}e - \frac{2348}{293}$ |
| 61 | $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ | $-\frac{38}{293}e^{3} - \frac{101}{293}e^{2} + \frac{818}{293}e + \frac{76}{293}$ |
| 61 | $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ | $-\frac{29}{293}e^{3} + \frac{54}{293}e^{2} + \frac{871}{293}e - \frac{1700}{293}$ |
| 61 | $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ | $\phantom{-}\frac{43}{293}e^{3} + \frac{122}{293}e^{2} - \frac{1049}{293}e - \frac{1844}{293}$ |
| 71 | $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ | $\phantom{-}\frac{29}{293}e^{3} - \frac{54}{293}e^{2} - \frac{1457}{293}e + \frac{1407}{293}$ |
| 71 | $[71, 71, w^{2} - 8]$ | $-\frac{95}{293}e^{3} - \frac{106}{293}e^{2} + \frac{2631}{293}e + \frac{483}{293}$ |
| 79 | $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ | $\phantom{-}\frac{23}{293}e^{3} + \frac{38}{293}e^{2} - \frac{711}{293}e - \frac{3269}{293}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ | $1$ |
| $5$ | $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ | $-1$ |