Properties

Label 4.4.14272.1-9.1-c
Base field 4.4.14272.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 9, w^{2} - 2w - 3]$
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: $[9, 9, w^{2} - 2w - 3]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 4x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + 3w^{2} + w - 2]$ $\phantom{-}2$
11 $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $-\frac{1}{2}e + 1$
13 $[13, 13, -w + 2]$ $\phantom{-}e - 2$
17 $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ $-\frac{3}{2}e + 5$
19 $[19, 19, -w^{2} + w + 4]$ $\phantom{-}e$
19 $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ $-e + 6$
23 $[23, 23, w^{2} - 2w - 1]$ $-e + 2$
27 $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ $-2e + 8$
29 $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ $-\frac{1}{2}e - 3$
37 $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ $-\frac{5}{2}e + 9$
41 $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ $\phantom{-}\frac{7}{2}e - 5$
53 $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ $-2$
59 $[59, 59, w - 4]$ $-e + 8$
67 $[67, 67, 2w^{2} - 3w - 8]$ $-e + 8$
73 $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ $-\frac{1}{2}e - 5$
89 $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ $-\frac{1}{2}e - 9$
97 $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ $\phantom{-}4e - 10$
97 $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e + 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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