Base field 4.4.7600.1
Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, 2w^{2} - 9]$ |
Dimension: | $10$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 38x^{8} + 469x^{6} - 2056x^{4} + 3008x^{2} - 512\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
9 | $[9, 3, -w^{2} - w + 4]$ | $-\frac{9}{832}e^{9} + \frac{11}{32}e^{7} - \frac{2765}{832}e^{5} + \frac{503}{52}e^{3} - \frac{181}{26}e$ |
9 | $[9, 3, w^{2} - w - 4]$ | $-\frac{9}{832}e^{9} + \frac{11}{32}e^{7} - \frac{2765}{832}e^{5} + \frac{503}{52}e^{3} - \frac{181}{26}e$ |
11 | $[11, 11, w + 1]$ | $-\frac{1}{208}e^{9} + \frac{3}{16}e^{7} - \frac{443}{208}e^{5} + \frac{1277}{208}e^{3} - \frac{105}{26}e$ |
11 | $[11, 11, w - 1]$ | $-\frac{1}{208}e^{9} + \frac{3}{16}e^{7} - \frac{443}{208}e^{5} + \frac{1277}{208}e^{3} - \frac{105}{26}e$ |
19 | $[19, 19, -w]$ | $\phantom{-}\frac{1}{832}e^{9} + \frac{1}{32}e^{7} - \frac{1195}{832}e^{5} + \frac{1207}{104}e^{3} - \frac{281}{13}e$ |
19 | $[19, 19, -w^{2} - w + 6]$ | $-\frac{3}{416}e^{8} + \frac{5}{16}e^{6} - \frac{1615}{416}e^{4} + \frac{643}{52}e^{2} - \frac{56}{13}$ |
19 | $[19, 19, -w^{2} + w + 6]$ | $-\frac{3}{416}e^{8} + \frac{5}{16}e^{6} - \frac{1615}{416}e^{4} + \frac{643}{52}e^{2} - \frac{56}{13}$ |
25 | $[25, 5, 2w^{2} - 9]$ | $-1$ |
29 | $[29, 29, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{7}{416}e^{8} - \frac{5}{16}e^{6} + \frac{371}{416}e^{4} - \frac{23}{13}e^{2} + \frac{70}{13}$ |
29 | $[29, 29, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{7}{416}e^{8} - \frac{5}{16}e^{6} + \frac{371}{416}e^{4} - \frac{23}{13}e^{2} + \frac{70}{13}$ |
41 | $[41, 41, 2w^{2} - w - 7]$ | $\phantom{-}\frac{7}{832}e^{9} - \frac{11}{32}e^{7} + \frac{3595}{832}e^{5} - \frac{3551}{208}e^{3} + \frac{269}{13}e$ |
41 | $[41, 41, w^{3} - w^{2} - 6w + 4]$ | $\phantom{-}\frac{7}{832}e^{9} - \frac{11}{32}e^{7} + \frac{3595}{832}e^{5} - \frac{3551}{208}e^{3} + \frac{269}{13}e$ |
61 | $[61, 61, -w^{3} + 3w^{2} + 6w - 14]$ | $-\frac{3}{416}e^{9} + \frac{1}{4}e^{7} - \frac{1043}{416}e^{5} + \frac{1155}{208}e^{3} - \frac{17}{13}e$ |
61 | $[61, 61, w^{3} + 2w^{2} - 5w - 8]$ | $\phantom{-}\frac{1}{52}e^{9} - \frac{11}{16}e^{7} + \frac{795}{104}e^{5} - \frac{5459}{208}e^{3} + \frac{275}{13}e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 8]$ | $\phantom{-}\frac{1}{52}e^{9} - \frac{11}{16}e^{7} + \frac{795}{104}e^{5} - \frac{5459}{208}e^{3} + \frac{275}{13}e$ |
61 | $[61, 61, w^{3} + 3w^{2} - 6w - 14]$ | $-\frac{3}{416}e^{9} + \frac{1}{4}e^{7} - \frac{1043}{416}e^{5} + \frac{1155}{208}e^{3} - \frac{17}{13}e$ |
89 | $[89, 89, -w^{3} + w^{2} + 6w - 9]$ | $-\frac{7}{416}e^{8} + \frac{5}{16}e^{6} - \frac{163}{416}e^{4} - \frac{175}{26}e^{2} + \frac{190}{13}$ |
89 | $[89, 89, 2w^{3} - w^{2} - 10w + 10]$ | $-\frac{7}{416}e^{8} + \frac{5}{16}e^{6} - \frac{163}{416}e^{4} - \frac{175}{26}e^{2} + \frac{190}{13}$ |
109 | $[109, 109, -w^{3} + 5w^{2} + 7w - 23]$ | $\phantom{-}\frac{1}{208}e^{9} - \frac{1}{4}e^{7} + \frac{625}{208}e^{5} - \frac{359}{104}e^{3} - \frac{415}{26}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, 2w^{2} - 9]$ | $1$ |