Base field 4.4.13625.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20,10,\frac{1}{2}w^{2} + \frac{1}{2}w - \frac{7}{2}]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 19x^{4} + 38x^{3} + 77x^{2} - 180x + 53\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ | $-\frac{1}{2}e^{5} + \frac{19}{2}e^{3} - \frac{1}{2}e^{2} - 39e + \frac{37}{2}$ |
| 11 | $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ | $-\frac{1}{8}e^{5} - \frac{1}{8}e^{4} + \frac{5}{2}e^{3} + \frac{7}{4}e^{2} - \frac{83}{8}e + \frac{3}{8}$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{9}{2}e^{3} + 3e^{2} + \frac{69}{4}e - \frac{47}{4}$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}\frac{1}{8}e^{5} + \frac{1}{8}e^{4} - 2e^{3} - \frac{9}{4}e^{2} + \frac{47}{8}e + \frac{33}{8}$ |
| 31 | $[31, 31, w]$ | $\phantom{-}\frac{1}{2}e^{5} - 9e^{3} - e^{2} + \frac{67}{2}e - 4$ |
| 31 | $[31, 31, w + 3]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e - \frac{9}{2}$ |
| 31 | $[31, 31, -w + 4]$ | $\phantom{-}\frac{3}{8}e^{5} - \frac{1}{8}e^{4} - 7e^{3} + \frac{9}{4}e^{2} + \frac{221}{8}e - \frac{105}{8}$ |
| 31 | $[31, 31, w - 1]$ | $\phantom{-}\frac{1}{8}e^{5} + \frac{1}{8}e^{4} - 3e^{3} - \frac{5}{4}e^{2} + \frac{135}{8}e - \frac{23}{8}$ |
| 41 | $[41, 41, -w^{2} + 2]$ | $\phantom{-}\frac{7}{8}e^{5} - \frac{1}{8}e^{4} - 16e^{3} + \frac{1}{4}e^{2} + \frac{489}{8}e - \frac{113}{8}$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ | $-e^{5} + 19e^{3} - 78e + 30$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - \frac{9}{2}e^{3} + 3e^{2} + \frac{73}{4}e - \frac{35}{4}$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ | $-\frac{1}{8}e^{5} - \frac{1}{8}e^{4} + 2e^{3} + \frac{13}{4}e^{2} - \frac{47}{8}e - \frac{105}{8}$ |
| 79 | $[79, 79, -w^{2} + 8]$ | $-\frac{3}{4}e^{5} + \frac{1}{4}e^{4} + 15e^{3} - \frac{9}{2}e^{2} - \frac{265}{4}e + \frac{145}{4}$ |
| 79 | $[79, 79, w^{2} - 2w - 7]$ | $\phantom{-}\frac{1}{8}e^{5} + \frac{1}{8}e^{4} - 3e^{3} - \frac{5}{4}e^{2} + \frac{119}{8}e - \frac{71}{8}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{2} - 7$ |
| 101 | $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ | $\phantom{-}e^{5} - 19e^{3} + e^{2} + 76e - 29$ |
| 101 | $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ | $-\frac{7}{8}e^{5} + \frac{1}{8}e^{4} + \frac{33}{2}e^{3} - \frac{15}{4}e^{2} - \frac{517}{8}e + \frac{325}{8}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,-\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ | $-1$ |
| $5$ | $[5,5,-w - 2]$ | $-1$ |