Properties

Label 3.3.1708.1-8.1-c
Base field 3.3.1708.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $3$
CM no
Base change no

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Base field 3.3.1708.1

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

Form

Weight: $[2, 2, 2]$
Level: $[8, 2, 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 3x^{2} - 9x + 18\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}0$
2 $[2, 2, w^{2} - 2w - 5]$ $-1$
5 $[5, 5, w^{2} + 3w + 1]$ $\phantom{-}e$
7 $[7, 7, -2w^{2} + 2w + 17]$ $\phantom{-}\frac{1}{3}e^{2} - 4$
7 $[7, 7, -w^{2} + w + 9]$ $\phantom{-}\frac{1}{3}e^{2} - 4$
13 $[13, 13, 2w + 1]$ $\phantom{-}\frac{1}{3}e^{2} - e - 4$
25 $[25, 5, -3w^{2} + 5w + 19]$ $\phantom{-}\frac{1}{3}e^{2} + e - 4$
27 $[27, 3, 3]$ $-e^{2} + e + 10$
29 $[29, 29, w^{2} + w - 1]$ $\phantom{-}e$
31 $[31, 31, w^{2} - w - 1]$ $\phantom{-}\frac{4}{3}e^{2} - e - 10$
37 $[37, 37, 2w^{2} + 6w + 3]$ $\phantom{-}\frac{4}{3}e^{2} - 2e - 10$
41 $[41, 41, -6w^{2} - 14w - 3]$ $\phantom{-}e^{2} - e - 12$
53 $[53, 53, -4w^{2} + 6w + 27]$ $-e$
59 $[59, 59, 2w^{2} - 4w - 11]$ $-e^{2} + 5e + 6$
61 $[61, 61, w^{2} - w - 3]$ $-\frac{5}{3}e^{2} + 3e + 8$
61 $[61, 61, -2w^{2} + 2w + 13]$ $\phantom{-}\frac{1}{3}e^{2} - 2e + 2$
73 $[73, 73, w^{2} + 3w + 3]$ $-e^{2} + 14$
97 $[97, 97, w^{2} + w - 15]$ $\phantom{-}\frac{1}{3}e^{2} - e - 16$
101 $[101, 101, w^{2} + 3w - 1]$ $\phantom{-}e^{2} - 5e - 12$
101 $[101, 101, w^{2} - w - 11]$ $\phantom{-}e^{2} - 2e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $-1$
$2$ $[2, 2, w^{2} - 2w - 5]$ $1$