Base field 4.4.11197.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[23, 23, -w^{2} + 3]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 38x^{6} + 380x^{4} - 744x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{3}{332}e^{7} - \frac{223}{664}e^{5} + \frac{527}{166}e^{3} - \frac{829}{166}e$ |
7 | $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}e$ |
11 | $[11, 11, -w - 2]$ | $\phantom{-}\frac{9}{1328}e^{6} - \frac{47}{166}e^{4} + \frac{915}{332}e^{2} - \frac{176}{83}$ |
11 | $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{19}{1328}e^{7} + \frac{45}{83}e^{5} - \frac{869}{166}e^{3} + \frac{1195}{166}e$ |
13 | $[13, 13, -w^{2} + 2w + 2]$ | $-\frac{43}{1328}e^{7} + \frac{403}{332}e^{5} - \frac{3929}{332}e^{3} + \frac{1717}{83}e$ |
16 | $[16, 2, 2]$ | $-\frac{9}{1328}e^{6} + \frac{47}{166}e^{4} - \frac{915}{332}e^{2} - \frac{73}{83}$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{33}{1328}e^{7} - \frac{317}{332}e^{5} + \frac{3189}{332}e^{3} - \frac{1503}{83}e$ |
23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}\frac{31}{1328}e^{7} - \frac{583}{664}e^{5} + \frac{2875}{332}e^{3} - \frac{2771}{166}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}1$ |
27 | $[27, 3, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}\frac{13}{664}e^{7} - \frac{497}{664}e^{5} + \frac{2505}{332}e^{3} - \frac{1237}{83}e$ |
29 | $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ | $-\frac{7}{664}e^{7} + \frac{137}{332}e^{5} - \frac{1451}{332}e^{3} + \frac{1811}{166}e$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $-\frac{33}{1328}e^{7} + \frac{317}{332}e^{5} - \frac{818}{83}e^{3} + \frac{3587}{166}e$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ | $-\frac{3}{664}e^{6} + \frac{35}{332}e^{4} - \frac{28}{83}e^{2} - \frac{602}{83}$ |
47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}\frac{61}{1328}e^{7} - \frac{591}{332}e^{5} + \frac{3087}{166}e^{3} - \frac{6877}{166}e$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ | $-\frac{21}{664}e^{6} + \frac{411}{332}e^{4} - \frac{1026}{83}e^{2} + \frac{1098}{83}$ |
67 | $[67, 67, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{25}{1328}e^{6} + \frac{215}{332}e^{4} - \frac{1933}{332}e^{2} + \frac{286}{83}$ |
67 | $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ | $\phantom{-}\frac{41}{1328}e^{6} - \frac{84}{83}e^{4} + \frac{2619}{332}e^{2} - \frac{894}{83}$ |
83 | $[83, 83, -2w + 3]$ | $-\frac{23}{664}e^{6} + \frac{379}{332}e^{4} - \frac{685}{83}e^{2} + \frac{254}{83}$ |
89 | $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ | $\phantom{-}\frac{61}{664}e^{7} - \frac{2281}{664}e^{5} + \frac{2755}{83}e^{3} - \frac{9687}{166}e$ |
97 | $[97, 97, w^{3} - w^{2} - 4w - 3]$ | $\phantom{-}\frac{21}{664}e^{6} - \frac{82}{83}e^{4} + \frac{1139}{166}e^{2} - \frac{600}{83}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, -w^{2} + 3]$ | $-1$ |