Properties

Label 3.3.1489.1-19.3-j
Base field 3.3.1489.1
Weight $[2, 2, 2]$
Level norm $19$
Level $[19, 19, -w + 3]$
Dimension $11$
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: $[19, 19, -w + 3]$
Dimension: $11$
CM: no
Base change: no
Newspace dimension: $38$

Hecke eigenvalues ($q$-expansion)

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

\(x^{11} + 2x^{10} - 66x^{9} - 104x^{8} + 1552x^{7} + 1620x^{6} - 15560x^{5} - 6720x^{4} + 62464x^{3} - 1024x^{2} - 71680x + 16384\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$19$ $[19, 19, -w + 3]$ $-1$