Properties

Label 4.4.14272.1-13.2-b
Base field 4.4.14272.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, -w + 2]$
Dimension $3$
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: $[13, 13, -w + 2]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 2x^{2} - x + 1\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, -w + 2]$ $1$