Properties

Label 3.3.1369.1-11.2-c
Base field 3.3.1369.1
Weight $[2, 2, 2]$
Level norm $11$
Level $[11,11,w^{2} - 3w - 7]$
Dimension $12$
CM no
Base change no

Related objects

Downloads

Learn more

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: $[11,11,w^{2} - 3w - 7]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 64x^{10} + 1492x^{8} + 219x^{7} - 15257x^{6} - 7355x^{5} + 63200x^{4} + 64940x^{3} - 57224x^{2} - 99360x - 33984\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11,11,w^{2} - 3w - 7]$ $-1$