Properties

Label 3.3.1436.1-9.1-a
Base field 3.3.1436.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 3, -w^{2} + 3w + 5]$
Dimension $17$
CM no
Base change no

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Base field 3.3.1436.1

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

Form

Weight: $[2, 2, 2]$
Level: $[9, 3, -w^{2} + 3w + 5]$
Dimension: $17$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{17} + 2x^{16} - 24x^{15} - 46x^{14} + 230x^{13} + 420x^{12} - 1123x^{11} - 1937x^{10} + 2948x^{9} + 4734x^{8} - 4010x^{7} - 5848x^{6} + 2433x^{5} + 3107x^{4} - 369x^{3} - 415x^{2} + 22x + 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $...$
3 $[3, 3, w^{2} - w - 9]$ $...$
9 $[9, 3, -w^{2} + 3w + 5]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + w + 11]$ $...$
13 $[13, 13, 2w^{2} - 4w - 13]$ $...$
23 $[23, 23, -w^{2} + w + 7]$ $...$
29 $[29, 29, -w^{2} - w + 1]$ $...$
41 $[41, 41, -2w^{2} + 2w + 19]$ $...$
41 $[41, 41, w^{2} - 3w - 7]$ $...$
41 $[41, 41, w^{2} - w - 5]$ $...$
47 $[47, 47, 3w^{2} - 7w - 17]$ $...$
53 $[53, 53, -2w - 1]$ $...$
61 $[61, 61, -2w + 7]$ $...$
67 $[67, 67, 3w^{2} - 5w - 23]$ $...$
67 $[67, 67, 2w^{2} - 4w - 11]$ $...$
67 $[67, 67, 3w^{2} - 7w - 13]$ $...$
79 $[79, 79, w^{2} + w - 5]$ $...$
89 $[89, 89, 5w^{2} - 7w - 47]$ $...$
97 $[97, 97, 5w^{2} - 11w - 29]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, -w^{2} + 3w + 5]$ $-1$