Properties

Label 4.4.16357.1-5.1-b
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $5$
Level $[5, 5, -w^{3} + 5w + 2]$
Dimension $4$
CM no
Base change no

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Base field 4.4.16357.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[5, 5, -w^{3} + 5w + 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 4x^{3} - 8x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $\phantom{-}e^{3} + 3e^{2} - 2e - 4$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}e - 2$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $\phantom{-}e^{2} + e - 4$
16 $[16, 2, 2]$ $-e - 3$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $-e^{3} - 3e^{2} + e + 4$
25 $[25, 5, -w^{2} + w + 3]$ $-e^{3} - 4e^{2} + 2$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $-e^{3} - 4e^{2} - 2e + 6$
31 $[31, 31, -w - 3]$ $-2e^{3} - 8e^{2} + 10$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-4$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}2e^{3} + 5e^{2} - 5e - 8$
43 $[43, 43, w^{3} - 7w - 2]$ $-e^{3} - e^{2} + 6e + 2$
47 $[47, 47, -2w^{3} + 11w + 2]$ $-2e^{2} - 4e - 2$
61 $[61, 61, w^{2} - 3]$ $\phantom{-}2e^{2} + 7e$
67 $[67, 67, w^{2} + w - 4]$ $-e^{3} - 3e^{2} + 6e + 6$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $\phantom{-}4e^{2} + 8e - 10$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $\phantom{-}2e^{3} + 8e^{2} - 2e - 16$
97 $[97, 97, -w^{3} + 6w - 3]$ $-e^{3} + e^{2} + 14e - 2$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}2e^{3} + 4e^{2} - 9e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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