Base field \(\Q(\sqrt{5}, \sqrt{17})\)
Generator \(w\), with minimal polynomial \(x^{4} - 11x^{2} + 9\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19,19,-\frac{1}{3}w^{3} + \frac{11}{3}w + 2]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} + 2x^{6} - 16x^{5} - 23x^{4} + 76x^{3} + 56x^{2} - 80x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{3}{2}]$ | $\phantom{-}e$ |
| 4 | $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{3}{2}]$ | $\phantom{-}\frac{1}{16}e^{6} + \frac{1}{4}e^{5} - e^{4} - \frac{55}{16}e^{3} + \frac{39}{8}e^{2} + \frac{43}{4}e - \frac{9}{2}$ |
| 9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{11}{3}w]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{1}{8}e^{5} - \frac{5}{4}e^{4} + \frac{17}{16}e^{3} + \frac{11}{2}e^{2} - \frac{1}{4}e - 1$ |
| 9 | $[9, 3, w]$ | $\phantom{-}\frac{3}{16}e^{6} + \frac{5}{8}e^{5} - \frac{9}{4}e^{4} - \frac{109}{16}e^{3} + \frac{17}{2}e^{2} + \frac{67}{4}e - 9$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}\frac{3}{16}e^{6} + \frac{3}{8}e^{5} - \frac{13}{4}e^{4} - \frac{77}{16}e^{3} + \frac{65}{4}e^{2} + \frac{53}{4}e - 12$ |
| 19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w - 2]$ | $-\frac{1}{4}e^{6} - \frac{3}{8}e^{5} + \frac{15}{4}e^{4} + \frac{17}{4}e^{3} - \frac{119}{8}e^{2} - 10e + \frac{19}{2}$ |
| 19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{11}{3}w + 2]$ | $-1$ |
| 19 | $[19, 19, -w + 2]$ | $\phantom{-}\frac{1}{8}e^{6} + \frac{1}{4}e^{5} - \frac{5}{2}e^{4} - \frac{39}{8}e^{3} + \frac{25}{2}e^{2} + \frac{41}{2}e - 10$ |
| 25 | $[25, 5, \frac{1}{3}w^{3} - \frac{8}{3}w]$ | $-\frac{1}{8}e^{6} - \frac{1}{4}e^{5} + \frac{3}{2}e^{4} + \frac{23}{8}e^{3} - \frac{7}{2}e^{2} - \frac{17}{2}e - 2$ |
| 49 | $[49, 7, \frac{2}{3}w^{3} - \frac{19}{3}w]$ | $-\frac{5}{16}e^{6} - \frac{7}{8}e^{5} + \frac{19}{4}e^{4} + \frac{155}{16}e^{3} - 22e^{2} - \frac{93}{4}e + 16$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{5}{3}w]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{1}{2}e^{5} - 4e^{4} - \frac{23}{4}e^{3} + 17e^{2} + 14e - 4$ |
| 59 | $[59, 59, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{11}{6}w]$ | $-\frac{1}{4}e^{6} - \frac{1}{2}e^{5} + 5e^{4} + \frac{31}{4}e^{3} - 27e^{2} - 27e + 22$ |
| 59 | $[59, 59, \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{11}{2}]$ | $\phantom{-}\frac{1}{4}e^{6} + e^{5} - 2e^{4} - \frac{39}{4}e^{3} + \frac{5}{2}e^{2} + 22e - 2$ |
| 59 | $[59, 59, \frac{1}{2}w^{2} - \frac{1}{2}w - \frac{11}{2}]$ | $\phantom{-}\frac{5}{16}e^{6} + \frac{7}{8}e^{5} - \frac{19}{4}e^{4} - \frac{155}{16}e^{3} + 22e^{2} + \frac{97}{4}e - 19$ |
| 59 | $[59, 59, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} - \frac{11}{6}w]$ | $\phantom{-}\frac{1}{8}e^{6} - 2e^{4} - \frac{7}{8}e^{3} + \frac{25}{4}e^{2} + \frac{15}{2}e + 5$ |
| 89 | $[89, 89, \frac{2}{3}w^{3} + \frac{1}{2}w^{2} - \frac{35}{6}w - \frac{7}{2}]$ | $-\frac{1}{2}e^{6} - \frac{9}{8}e^{5} + \frac{33}{4}e^{4} + 15e^{3} - \frac{289}{8}e^{2} - 46e + \frac{37}{2}$ |
| 89 | $[89, 89, -\frac{5}{6}w^{3} + \frac{26}{3}w - \frac{3}{2}]$ | $-\frac{1}{8}e^{6} - \frac{3}{4}e^{5} + \frac{5}{2}e^{4} + \frac{79}{8}e^{3} - 17e^{2} - \frac{57}{2}e + 24$ |
| 89 | $[89, 89, \frac{1}{6}w^{3} - \frac{1}{2}w^{2} + \frac{1}{6}w - 2]$ | $-\frac{1}{8}e^{6} - \frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{9}{8}e^{3} + \frac{5}{2}e^{2} + \frac{37}{2}e + 2$ |
| 89 | $[89, 89, -\frac{1}{6}w^{3} - w^{2} + \frac{7}{3}w + \frac{5}{2}]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{1}{4}e^{5} - \frac{5}{2}e^{4} + \frac{25}{8}e^{3} + 12e^{2} - \frac{17}{2}e - 6$ |
| 101 | $[101, 101, \frac{1}{6}w^{3} + \frac{1}{2}w^{2} - \frac{17}{6}w + 1]$ | $\phantom{-}\frac{7}{8}e^{6} + \frac{5}{2}e^{5} - 11e^{4} - \frac{217}{8}e^{3} + \frac{157}{4}e^{2} + \frac{137}{2}e - 31$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-\frac{1}{3}w^{3} + \frac{11}{3}w + 2]$ | $1$ |