Base field \(\Q(\sqrt{5}, \sqrt{7})\)
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 15x^{2} + 16x + 29\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $62$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 12x^{3} + 14x^{2} + 232x - 604\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ | $-2$ |
| 9 | $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ | $-\frac{1}{10}e^{3} + \frac{2}{5}e^{2} + \frac{14}{5}e - \frac{39}{5}$ |
| 9 | $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{2}{5}e^{2} - \frac{14}{5}e + \frac{29}{5}$ |
| 19 | $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ | $-\frac{4}{15}e^{3} + \frac{26}{15}e^{2} + \frac{29}{5}e - \frac{532}{15}$ |
| 19 | $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{2}{5}e^{2} - \frac{9}{5}e + \frac{4}{5}$ |
| 19 | $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ | $-\frac{1}{6}e^{3} + \frac{4}{3}e^{2} + 3e - \frac{68}{3}$ |
| 25 | $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w]$ | $-\frac{1}{30}e^{3} + \frac{1}{15}e^{2} + 2e - \frac{83}{15}$ |
| 29 | $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ | $-\frac{1}{6}e^{3} + \frac{11}{15}e^{2} + \frac{18}{5}e - \frac{181}{15}$ |
| 29 | $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{9}{5}e^{2} - \frac{34}{5}e + 31$ |
| 29 | $[29, 29, -w + 1]$ | $-\frac{1}{10}e^{3} + e^{2} + \frac{6}{5}e - \frac{107}{5}$ |
| 31 | $[31, 31, w + 2]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{11}{5}e^{2} - \frac{27}{5}e + \frac{192}{5}$ |
| 31 | $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{13}{5}e^{2} - \frac{41}{5}e + \frac{246}{5}$ |
| 31 | $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ | $-\frac{7}{30}e^{3} + \frac{19}{15}e^{2} + \frac{21}{5}e - \frac{248}{15}$ |
| 31 | $[31, 31, -w + 3]$ | $-\frac{2}{15}e^{3} + \frac{13}{15}e^{2} + \frac{7}{5}e - \frac{206}{15}$ |
| 49 | $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ | $\phantom{-}6$ |
| 59 | $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ | $\phantom{-}\frac{3}{10}e^{3} - 2e^{2} - \frac{28}{5}e + \frac{216}{5}$ |
| 59 | $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ | $\phantom{-}\frac{3}{10}e^{3} - 2e^{2} - \frac{28}{5}e + \frac{136}{5}$ |
| 59 | $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ | $-\frac{7}{30}e^{3} + \frac{22}{15}e^{2} + 4e - \frac{476}{15}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25,5,-\frac{4}{23}w^{3}+\frac{6}{23}w^{2}+\frac{40}{23}w-\frac{21}{23}]$ | $-1$ |