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