Properties

Label 3.3.1489.1-8.1-c
Base field 3.3.1489.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $2$
CM no
Base change no

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Base field 3.3.1489.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x - 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 2, 2]$
Dimension: $2$
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:

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w]$ $\phantom{-}2$
8 $[8, 2, 2]$ $-1$
13 $[13, 13, w^{2} - 3w - 5]$ $\phantom{-}e$
17 $[17, 17, w - 1]$ $\phantom{-}\frac{5}{2}e + 6$
19 $[19, 19, -w^{2} + 2w + 6]$ $-2e - 6$
19 $[19, 19, -w^{2} + 2w + 10]$ $\phantom{-}e - 3$
19 $[19, 19, -w + 3]$ $-\frac{1}{2}e - 4$
23 $[23, 23, w - 2]$ $-e - 2$
27 $[27, 3, 3]$ $-2e - 8$
29 $[29, 29, w^{2} - 2w - 5]$ $-6$
31 $[31, 31, w^{2} - 3w - 6]$ $-3e - 4$
31 $[31, 31, w^{2} - w - 8]$ $\phantom{-}3e + 8$
31 $[31, 31, w^{2} - 2w - 4]$ $-2e - 8$
41 $[41, 41, w^{2} - w - 5]$ $-\frac{3}{2}e + 4$
43 $[43, 43, w^{2} - 3w - 10]$ $-2e - 5$
47 $[47, 47, -w - 4]$ $\phantom{-}e + 2$
47 $[47, 47, w^{2} - w - 9]$ $-e - 10$
47 $[47, 47, -2w^{2} + 3w + 17]$ $\phantom{-}10$
49 $[49, 7, w^{2} - w - 10]$ $\phantom{-}\frac{1}{2}e - 4$
53 $[53, 53, w^{2} - w - 4]$ $\phantom{-}e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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