Properties

Label 4.4.14272.1-27.2-f
Base field 4.4.14272.1
Weight $[2, 2, 2, 2]$
Level norm $27$
Level $[27, 27, w^{3} - 2w^{2} - 3w]$
Dimension $2$
CM no
Base change no

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Base field 4.4.14272.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[27, 27, w^{3} - 2w^{2} - 3w]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - x - 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $\phantom{-}e$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}\frac{1}{3}e + \frac{1}{3}$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}\frac{1}{3}e + \frac{13}{3}$
13 $[13, 13, -w + 2]$ $-\frac{2}{3}e + \frac{1}{3}$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $-e + 4$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{3}e + \frac{1}{3}$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $-\frac{1}{3}e + \frac{17}{3}$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}\frac{5}{3}e + \frac{2}{3}$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $\phantom{-}\frac{1}{3}e - \frac{2}{3}$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $-\frac{2}{3}e - \frac{2}{3}$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $-\frac{4}{3}e - \frac{13}{3}$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{7}{3}e - \frac{4}{3}$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $-8$
59 $[59, 59, w - 4]$ $\phantom{-}\frac{8}{3}e - \frac{4}{3}$
67 $[67, 67, 2w^{2} - 3w - 8]$ $-\frac{4}{3}e + \frac{2}{3}$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $\phantom{-}\frac{4}{3}e + \frac{7}{3}$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $-\frac{5}{3}e + \frac{4}{3}$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $\phantom{-}\frac{4}{3}e - \frac{17}{3}$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $-\frac{4}{3}e + \frac{23}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$