Properties

Label 4.4.16448.1-10.1-f
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $10$
Level $[10, 10, w^{3} - 3w^{2} - 3w + 4]$
Dimension $3$
CM no
Base change no

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Base field 4.4.16448.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[10, 10, w^{3} - 3w^{2} - 3w + 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 3x^{2} - 6x - 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $-1$
5 $[5, 5, w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $-\frac{1}{3}e^{2}$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{3}e^{2} + e - 1$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $-\frac{2}{3}e^{2} + 6$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $\phantom{-}\frac{1}{3}e^{2} + 2e$
25 $[25, 5, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{3}e^{2} - e - 1$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $-\frac{2}{3}e^{2} - e$
31 $[31, 31, -w^{2} + 2w + 1]$ $-\frac{1}{3}e^{2} + e + 5$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $\phantom{-}\frac{2}{3}e^{2} + 3e + 2$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $\phantom{-}2e^{2} + 3e - 10$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $\phantom{-}\frac{2}{3}e^{2} + 6e$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $\phantom{-}\frac{4}{3}e^{2} + 2e - 10$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $-\frac{8}{3}e^{2} - 4e + 14$
81 $[81, 3, -3]$ $\phantom{-}\frac{5}{3}e^{2} + 4e - 2$
83 $[83, 83, -w - 3]$ $-2e^{2} - 6e + 6$
83 $[83, 83, w^{2} - 3w - 7]$ $-\frac{1}{3}e^{2} - e + 9$
89 $[89, 89, w^{2} - 2w - 7]$ $-\frac{7}{3}e^{2} - 4e + 12$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $\phantom{-}2e^{2} + 4e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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