Properties

Label 4.4.11197.1-23.2-b
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23, 23, -w^{2} + 3]$
Dimension $8$
CM no
Base change no

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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 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $\phantom{-}\frac{21}{664}e^{6} - \frac{82}{83}e^{4} + \frac{1139}{166}e^{2} - \frac{600}{83}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{2} + 3]$ $-1$