Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 3, w^{3} - w^{2} - 4w]$ |
Dimension: | $8$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 36x^{6} + 432x^{4} - 2020x^{2} + 3008\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{37}e^{6} - \frac{53}{74}e^{4} + \frac{171}{37}e^{2} - \frac{192}{37}$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{1}{37}e^{6} - \frac{53}{74}e^{4} + \frac{171}{37}e^{2} - \frac{192}{37}$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-1$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{7}{74}e^{6} - \frac{102}{37}e^{4} + \frac{839}{37}e^{2} - \frac{1819}{37}$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{3}{148}e^{7} + \frac{49}{74}e^{5} - \frac{230}{37}e^{3} + \frac{551}{37}e$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{3}{148}e^{7} + \frac{49}{74}e^{5} - \frac{230}{37}e^{3} + \frac{551}{37}e$ |
25 | $[25, 5, w^{2} - w - 3]$ | $\phantom{-}\frac{2}{37}e^{6} - \frac{53}{37}e^{4} + \frac{379}{37}e^{2} - \frac{606}{37}$ |
37 | $[37, 37, 2w - 1]$ | $-\frac{11}{74}e^{6} + \frac{155}{37}e^{4} - \frac{1218}{37}e^{2} + \frac{2462}{37}$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{3}{37}e^{6} + \frac{159}{74}e^{4} - \frac{587}{37}e^{2} + \frac{1316}{37}$ |
43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $-\frac{3}{37}e^{6} + \frac{159}{74}e^{4} - \frac{587}{37}e^{2} + \frac{1316}{37}$ |
59 | $[59, 59, 2w - 5]$ | $\phantom{-}\frac{1}{37}e^{7} - \frac{53}{74}e^{5} + \frac{171}{37}e^{3} - \frac{118}{37}e$ |
59 | $[59, 59, -2w - 3]$ | $\phantom{-}\frac{1}{37}e^{7} - \frac{53}{74}e^{5} + \frac{171}{37}e^{3} - \frac{118}{37}e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}\frac{1}{37}e^{6} - \frac{45}{37}e^{4} + \frac{504}{37}e^{2} - \frac{1080}{37}$ |
79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{1}{37}e^{6} - \frac{45}{37}e^{4} + \frac{504}{37}e^{2} - \frac{1080}{37}$ |
83 | $[83, 83, -w^{3} + 7w]$ | $-\frac{1}{37}e^{7} + \frac{53}{74}e^{5} - \frac{171}{37}e^{3} + \frac{266}{37}e$ |
83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{3}{74}e^{7} - \frac{49}{37}e^{5} + \frac{460}{37}e^{3} - \frac{1102}{37}e$ |
83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}\frac{3}{74}e^{7} - \frac{49}{37}e^{5} + \frac{460}{37}e^{3} - \frac{1102}{37}e$ |
83 | $[83, 83, w^{2} - 2w - 6]$ | $-\frac{1}{37}e^{7} + \frac{53}{74}e^{5} - \frac{171}{37}e^{3} + \frac{266}{37}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, w^{3} - w^{2} - 4w]$ | $1$ |