Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 5 x^2 + 3 x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 16, w^3 - 2 w^2 - 4 w]$ |
| Dimension: | $7$ |
| 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:
| \(x^7 - 4 x^6 - 17 x^5 + 72 x^4 + 29 x^3 - 198 x^2 + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^3 - 3 w^2 - w + 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^2 - 2 w - 3]$ | $\phantom{-}\frac{1}{16} e^6 - \frac{1}{8} e^5 - \frac{23}{16} e^4 + \frac{17}{8} e^3 + \frac{125}{16} e^2 - \frac{39}{8} e - 8$ |
| 5 | $[5, 5, w^3 - 3 w^2 - 3 w + 5]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^3 - 2 w^2 - 3 w + 3]$ | $\phantom{-}\frac{1}{16} e^6 - \frac{1}{8} e^5 - \frac{21}{16} e^4 + 2 e^3 + \frac{99}{16} e^2 - \frac{25}{8} e - 8$ |
| 13 | $[13, 13, -w^2 + w + 3]$ | $-\frac{1}{16} e^6 + \frac{1}{4} e^5 + \frac{15}{16} e^4 - \frac{31}{8} e^3 + \frac{5}{16} e^2 + \frac{25}{8} e - 4$ |
| 17 | $[17, 17, -w^2 + 3 w + 1]$ | $\phantom{-}\frac{1}{4} e^4 - \frac{1}{4} e^3 - \frac{17}{4} e^2 + \frac{7}{2} e + 8$ |
| 23 | $[23, 23, w^2 - 3]$ | $-\frac{1}{16} e^6 + \frac{1}{4} e^5 + \frac{17}{16} e^4 - \frac{9}{2} e^3 - \frac{29}{16} e^2 + \frac{83}{8} e$ |
| 25 | $[25, 5, -w^2 + 2 w + 1]$ | $-\frac{1}{8} e^6 + \frac{1}{2} e^5 + 2 e^4 - \frac{67}{8} e^3 - \frac{3}{2} e^2 + \frac{27}{2} e$ |
| 37 | $[37, 37, w^3 - 4 w^2 - 2 w + 9]$ | $\phantom{-}\frac{1}{8} e^6 - \frac{1}{2} e^5 - 2 e^4 + \frac{67}{8} e^3 + \frac{3}{2} e^2 - \frac{31}{2} e + 4$ |
| 41 | $[41, 41, w^2 - w - 5]$ | $\phantom{-}\frac{1}{8} e^5 - \frac{3}{8} e^4 - \frac{19}{8} e^3 + 6 e^2 + \frac{11}{2} e - 4$ |
| 49 | $[49, 7, -w^3 + 2 w^2 + 2 w - 1]$ | $-\frac{1}{8} e^6 + \frac{3}{8} e^5 + 2 e^4 - \frac{49}{8} e^3 - \frac{9}{8} e^2 + \frac{33}{4} e - 4$ |
| 49 | $[49, 7, w^2 + w - 3]$ | $-\frac{1}{8} e^5 + \frac{3}{8} e^4 + \frac{19}{8} e^3 - 6 e^2 - \frac{19}{2} e + 8$ |
| 59 | $[59, 59, w^3 - 3 w^2 - 4 w + 5]$ | $\phantom{-}\frac{1}{2} e^3 - \frac{1}{2} e^2 - \frac{9}{2} e + 5$ |
| 67 | $[67, 67, -w^3 + 3 w^2 + w - 5]$ | $\phantom{-}\frac{1}{4} e^6 - \frac{3}{4} e^5 - \frac{9}{2} e^4 + \frac{49}{4} e^3 + \frac{45}{4} e^2 - 17 e - 9$ |
| 71 | $[71, 71, 2 w - 3]$ | $-\frac{1}{8} e^6 + \frac{1}{4} e^5 + \frac{23}{8} e^4 - \frac{17}{4} e^3 - \frac{125}{8} e^2 + \frac{31}{4} e + 16$ |
| 71 | $[71, 71, w^3 - 4 w^2 + 2 w + 5]$ | $-\frac{1}{4} e^4 - \frac{1}{4} e^3 + \frac{15}{4} e^2 + 5 e - 3$ |
| 79 | $[79, 79, -w^3 + 5 w^2 - 4 w - 5]$ | $-\frac{1}{8} e^6 + \frac{1}{2} e^5 + \frac{17}{8} e^4 - 9 e^3 - \frac{29}{8} e^2 + \frac{91}{4} e + 4$ |
| 79 | $[79, 79, -2 w^3 + 7 w^2 + 5 w - 15]$ | $\phantom{-}\frac{1}{2} e^4 - \frac{1}{2} e^3 - \frac{17}{2} e^2 + 7 e + 12$ |
| 81 | $[81, 3, -3]$ | $-\frac{1}{4} e^6 + \frac{3}{4} e^5 + \frac{9}{2} e^4 - \frac{49}{4} e^3 - \frac{41}{4} e^2 + 17 e + 3$ |
| 83 | $[83, 83, -2 w^3 + 6 w^2 + 2 w - 5]$ | $-\frac{1}{2} e^4 + \frac{1}{2} e^3 + \frac{17}{2} e^2 - 5 e - 20$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^3 - 3 w^2 - w + 2]$ | $1$ |