Properties

Label 3.3.1492.1-11.1-b
Base field 3.3.1492.1
Weight $[2, 2, 2]$
Level norm $11$
Level $[11, 11, w^{2} - 2w - 2]$
Dimension $16$
CM no
Base change no

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Base field 3.3.1492.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[11, 11, w^{2} - 2w - 2]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $32$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} - 24x^{14} + 2x^{13} + 231x^{12} - 35x^{11} - 1140x^{10} + 233x^{9} + 3059x^{8} - 739x^{7} - 4357x^{6} + 1145x^{5} + 2958x^{4} - 787x^{3} - 713x^{2} + 186x + 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $\phantom{-}e$
5 $[5, 5, w]$ $...$
7 $[7, 7, w^{2} - 2w - 8]$ $...$
7 $[7, 7, -2w^{2} + 3w + 16]$ $...$
7 $[7, 7, -w^{2} + 2w + 6]$ $...$
11 $[11, 11, w^{2} - 2w - 2]$ $-1$
19 $[19, 19, -w + 2]$ $...$
23 $[23, 23, -w^{2} + 3w + 1]$ $...$
25 $[25, 5, w^{2} - w - 9]$ $...$
27 $[27, 3, 3]$ $...$
29 $[29, 29, -w^{2} - w + 1]$ $...$
29 $[29, 29, w^{2} - 2w - 4]$ $...$
29 $[29, 29, -w^{2} + w + 11]$ $...$
43 $[43, 43, 2w^{2} - 3w - 18]$ $...$
47 $[47, 47, -2w + 7]$ $...$
53 $[53, 53, w^{2} - w - 3]$ $...$
61 $[61, 61, w^{2} + 2w + 2]$ $...$
67 $[67, 67, -2w^{2} + 5w + 8]$ $...$
79 $[79, 79, w^{2} - 3w - 9]$ $...$
97 $[97, 97, -w^{2} - 2w + 2]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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