Base field 4.4.12197.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + w + 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 6x^{7} - 7x^{6} + 94x^{5} - 80x^{4} - 346x^{3} + 576x^{2} - 160x - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $-\frac{3}{8}e^{7} + e^{6} + \frac{49}{8}e^{5} - \frac{31}{2}e^{4} - \frac{47}{2}e^{3} + \frac{239}{4}e^{2} - \frac{27}{2}e - 10$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{3}{4}e^{6} - \frac{15}{4}e^{5} + \frac{45}{4}e^{4} + 12e^{3} - \frac{83}{2}e^{2} + \frac{33}{2}e + 5$ |
| 13 | $[13, 13, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{1}{2}e^{6} - \frac{17}{4}e^{5} + \frac{15}{2}e^{4} + \frac{35}{2}e^{3} - \frac{55}{2}e^{2} + 6e + 1$ |
| 16 | $[16, 2, 2]$ | $-\frac{3}{8}e^{7} + \frac{3}{4}e^{6} + \frac{53}{8}e^{5} - \frac{43}{4}e^{4} - 31e^{3} + \frac{147}{4}e^{2} + 11e - 7$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-1$ |
| 19 | $[19, 19, w^{3} - 5w]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{1}{2}e^{5} - \frac{15}{4}e^{4} + \frac{13}{2}e^{3} + 14e^{2} - \frac{39}{2}e$ |
| 19 | $[19, 19, -w + 3]$ | $\phantom{-}\frac{5}{8}e^{7} - 2e^{6} - \frac{75}{8}e^{5} + \frac{61}{2}e^{4} + 29e^{3} - \frac{461}{4}e^{2} + \frac{101}{2}e + 15$ |
| 23 | $[23, 23, 2w^{3} - 2w^{2} - 9w + 4]$ | $\phantom{-}\frac{5}{8}e^{7} - \frac{7}{4}e^{6} - \frac{79}{8}e^{5} + \frac{107}{4}e^{4} + \frac{69}{2}e^{3} - \frac{405}{4}e^{2} + 39e + 15$ |
| 23 | $[23, 23, w^{2} - 2]$ | $\phantom{-}\frac{7}{8}e^{7} - \frac{11}{4}e^{6} - \frac{109}{8}e^{5} + \frac{171}{4}e^{4} + \frac{91}{2}e^{3} - \frac{663}{4}e^{2} + 67e + 27$ |
| 25 | $[25, 5, w^{2} - 3]$ | $-\frac{3}{4}e^{7} + 2e^{6} + \frac{49}{4}e^{5} - 31e^{4} - 46e^{3} + \frac{237}{2}e^{2} - 37e - 12$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 6]$ | $\phantom{-}\frac{5}{8}e^{7} - 2e^{6} - \frac{75}{8}e^{5} + \frac{63}{2}e^{4} + 27e^{3} - \frac{493}{4}e^{2} + \frac{129}{2}e + 13$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 4]$ | $-\frac{1}{2}e^{7} + \frac{5}{4}e^{6} + 8e^{5} - \frac{75}{4}e^{4} - \frac{59}{2}e^{3} + 69e^{2} - \frac{41}{2}e - 8$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{5}{4}e^{6} - 8e^{5} + \frac{71}{4}e^{4} + \frac{63}{2}e^{3} - 61e^{2} + \frac{15}{2}e + 12$ |
| 47 | $[47, 47, w^{3} - 6w + 1]$ | $\phantom{-}\frac{3}{4}e^{7} - 2e^{6} - \frac{49}{4}e^{5} + 30e^{4} + 47e^{3} - \frac{219}{2}e^{2} + 31e + 16$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{1}{2}e^{6} - e^{5} - \frac{17}{2}e^{4} + 14e^{3} + 36e^{2} - 45e$ |
| 67 | $[67, 67, 2w^{3} - w^{2} - 9w + 2]$ | $-\frac{13}{8}e^{7} + 5e^{6} + \frac{203}{8}e^{5} - \frac{155}{2}e^{4} - 85e^{3} + \frac{1189}{4}e^{2} - \frac{239}{2}e - 41$ |
| 67 | $[67, 67, w^{3} - 7w + 3]$ | $-\frac{7}{4}e^{7} + \frac{9}{2}e^{6} + \frac{115}{4}e^{5} - \frac{137}{2}e^{4} - \frac{223}{2}e^{3} + \frac{513}{2}e^{2} - 66e - 39$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w]$ | $\phantom{-}\frac{3}{4}e^{7} - \frac{7}{4}e^{6} - \frac{51}{4}e^{5} + \frac{101}{4}e^{4} + \frac{111}{2}e^{3} - \frac{175}{2}e^{2} - \frac{3}{2}e + 16$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{11}{8}e^{7} - \frac{7}{2}e^{6} - \frac{177}{8}e^{5} + 51e^{4} + \frac{167}{2}e^{3} - \frac{711}{4}e^{2} + \frac{113}{2}e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + w + 3]$ | $1$ |