Properties

Label 3.3.1257.1-8.1-a
Base field 3.3.1257.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1257.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 9\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 2, 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{4} - 8x^{2} + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 3]$ $-1$
3 $[3, 3, w - 2]$ $\phantom{-}e$
5 $[5, 5, w^{2} + w - 5]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-1$
13 $[13, 13, w + 2]$ $-e^{2} + 1$
13 $[13, 13, -2w + 5]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e$
13 $[13, 13, -w^{2} - w + 4]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e$
19 $[19, 19, -w^{2} + w + 4]$ $-\frac{3}{2}e^{3} + \frac{23}{2}e$
23 $[23, 23, -w^{2} - w + 7]$ $\phantom{-}e^{3} - 10e$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e$
29 $[29, 29, w^{2} - 5]$ $-e^{3} + 6e$
31 $[31, 31, w^{2} + w - 8]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e$
41 $[41, 41, w^{2} + w - 11]$ $\phantom{-}0$
47 $[47, 47, w^{2} + 2w - 1]$ $-\frac{5}{2}e^{2} + \frac{15}{2}$
59 $[59, 59, w^{2} + w - 1]$ $-\frac{3}{2}e^{2} + \frac{15}{2}$
61 $[61, 61, -w^{2} + 5w - 7]$ $-\frac{5}{2}e^{2} + \frac{13}{2}$
67 $[67, 67, 2w^{2} - 13]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{33}{2}e$
89 $[89, 89, -2w^{2} + w + 20]$ $\phantom{-}3e^{2} - 12$
89 $[89, 89, 5w^{2} + 8w - 19]$ $\phantom{-}e^{3} - 5e$
89 $[89, 89, w^{2} + 2w - 7]$ $-4e^{3} + 26e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$8$ $[8, 2, 2]$ $1$