Properties

Label 4.4.11197.1-27.1-b
Base field 4.4.11197.1
Weight $[2, 2, 2, 2]$
Level norm $27$
Level $[27, 3, w^{3} - 3w^{2} - w + 4]$
Dimension $14$
CM no
Base change no

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Base field 4.4.11197.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 3x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[27, 3, w^{3} - 3w^{2} - w + 4]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} + 6x^{13} - 7x^{12} - 96x^{11} - 50x^{10} + 576x^{9} + 642x^{8} - 1568x^{7} - 2330x^{6} + 1794x^{5} + 3467x^{4} - 494x^{3} - 1868x^{2} - 84x + 284\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w^{3} - 2w^{2} - 3w + 1]$ $...$
11 $[11, 11, -w - 2]$ $...$
11 $[11, 11, -w^{3} + 2w^{2} + 3w - 2]$ $...$
13 $[13, 13, -w^{2} + 2w + 2]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $...$
23 $[23, 23, -w^{2} + w + 3]$ $...$
23 $[23, 23, -w^{2} + 3]$ $...$
27 $[27, 3, w^{3} - 3w^{2} - w + 4]$ $\phantom{-}1$
29 $[29, 29, -w^{3} + 3w^{2} + 3w - 5]$ $...$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $...$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 5]$ $...$
47 $[47, 47, w^{2} - 3w - 2]$ $...$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $...$
67 $[67, 67, -w^{3} + w^{2} + 5w - 1]$ $...$
67 $[67, 67, -2w^{3} + 3w^{2} + 11w - 7]$ $...$
83 $[83, 83, -2w + 3]$ $...$
89 $[89, 89, 3w^{3} - 7w^{2} - 9w + 9]$ $...$
97 $[97, 97, w^{3} - w^{2} - 4w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$27$ $[27, 3, w^{3} - 3w^{2} - w + 4]$ $-1$