Properties

Label 4.4.17989.1-13.1-a
Base field 4.4.17989.1
Weight $[2, 2, 2, 2]$
Level norm $13$
Level $[13, 13, w^{2} - 3w - 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.17989.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[13, 13, w^{2} - 3w - 2]$
Dimension: $4$
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:

\(x^{4} - x^{3} - 7x^{2} + 3x + 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ $-e^{2} + e + 5$
11 $[11, 11, w^{3} - 2w^{2} - 4w]$ $\phantom{-}e^{3} - 2e^{2} - 3e + 3$
13 $[13, 13, w^{2} - 3w - 2]$ $-1$
16 $[16, 2, 2]$ $\phantom{-}e^{3} - 2e^{2} - 2e + 4$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}e^{2} - 2e$
17 $[17, 17, -w^{2} + 2w + 3]$ $-e^{2} + 4$
23 $[23, 23, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}e^{3} - 5e + 2$
27 $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ $-e^{3} + 3e^{2} + 4e - 7$
29 $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ $-e^{2} - e + 9$
31 $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ $-2e^{3} + 4e^{2} + 8e - 10$
31 $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ $\phantom{-}2e^{3} - 2e^{2} - 7e + 3$
31 $[31, 31, w^{3} - 2w^{2} - 6w]$ $-e^{2} - 2e + 8$
31 $[31, 31, -w^{2} + 2w + 1]$ $-2e^{3} + 3e^{2} + 9e - 8$
37 $[37, 37, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}2e^{3} - 4e^{2} - 6e + 12$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}e + 7$
71 $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ $\phantom{-}e^{3} - 5e^{2} + e + 16$
71 $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ $\phantom{-}2e^{3} - 6e^{2} - 4e + 22$
89 $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ $\phantom{-}e^{3} + 3e^{2} - 6e - 11$
97 $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ $-e^{3} + 4e^{2} - 2e - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w^{2} - 3w - 2]$ $1$