Properties

Label 3.3.1369.1-8.1-c
Base field 3.3.1369.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 2, 2]$
Dimension $3$
CM no
Base change yes

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Base field 3.3.1369.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 2, 2]$
Dimension: $3$
CM: no
Base change: yes
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 4x^{2} - 16x + 48\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, 2]$ $\phantom{-}1$
11 $[11, 11, w]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 3w + 7]$ $\phantom{-}e$
11 $[11, 11, w^{2} - 2w - 8]$ $\phantom{-}e$
23 $[23, 23, w^{2} - 2w - 7]$ $\phantom{-}\frac{1}{4}e^{2} - e$
23 $[23, 23, w^{2} - 3w - 8]$ $\phantom{-}\frac{1}{4}e^{2} - e$
23 $[23, 23, w - 1]$ $\phantom{-}\frac{1}{4}e^{2} - e$
27 $[27, 3, 3]$ $\phantom{-}\frac{1}{4}e^{2} - 8$
29 $[29, 29, w^{2} - 2w - 5]$ $-\frac{1}{4}e^{2} + 3$
29 $[29, 29, w^{2} - 3w - 10]$ $-\frac{1}{4}e^{2} + 3$
29 $[29, 29, w - 3]$ $-\frac{1}{4}e^{2} + 3$
31 $[31, 31, w^{2} - 2w - 6]$ $-\frac{1}{2}e^{2} + e + 8$
31 $[31, 31, -w^{2} + 3w + 9]$ $-\frac{1}{2}e^{2} + e + 8$
31 $[31, 31, w - 2]$ $-\frac{1}{2}e^{2} + e + 8$
37 $[37, 37, -w^{2} + 4w + 7]$ $-\frac{1}{4}e^{2} + e - 1$
43 $[43, 43, 2w^{2} - 6w - 13]$ $-\frac{1}{4}e^{2} - e + 8$
43 $[43, 43, 2w^{2} - 4w - 17]$ $-\frac{1}{4}e^{2} - e + 8$
43 $[43, 43, w^{2} - 2w - 12]$ $-\frac{1}{4}e^{2} - e + 8$
47 $[47, 47, w^{2} - 4w - 4]$ $\phantom{-}\frac{1}{2}e^{2} - e - 12$
47 $[47, 47, w^{2} - w - 5]$ $\phantom{-}\frac{1}{2}e^{2} - e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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