Properties

Base field 4.4.16997.1
Weight [2, 2, 2, 2]
Level norm 25
Level $[25, 25, -w^{3} + 5w + 3]$
Label 4.4.16997.1-25.3-g
Dimension 4
CM no
Base change no

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Base field 4.4.16997.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[25, 25, -w^{3} + 5w + 3]$
Label 4.4.16997.1-25.3-g
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 39

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 7x^{2} + 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}e^{2} - 3$
5 $[5, 5, -w^{2} + w + 2]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $-e^{3} + 5e + 1$
13 $[13, 13, w^{2} - w - 4]$ $\phantom{-}e^{2} + 2e - 5$
16 $[16, 2, 2]$ $\phantom{-}e^{3} + e^{2} - 4e - 3$
19 $[19, 19, -w^{2} + w + 1]$ $-2e^{2} + e + 6$
23 $[23, 23, -w^{3} + 4w + 2]$ $-2e^{2} + 2e + 8$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}e^{2} - e + 1$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e^{2} - 2e - 2$
29 $[29, 29, -w + 3]$ $\phantom{-}e^{3} + e^{2} - 5e - 3$
31 $[31, 31, -w^{3} + w^{2} + 5w - 2]$ $-e^{3} + 2e^{2} + 5e - 4$
37 $[37, 37, w^{3} - 4w - 1]$ $\phantom{-}e^{2} - 4e - 7$
37 $[37, 37, w^{3} - 3w + 1]$ $-e^{3} + e^{2} + 5e - 1$
53 $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ $-e^{3} + e^{2} + 3e - 7$
59 $[59, 59, w^{2} + w - 4]$ $-e^{3} + 2e^{2} + 5e - 6$
61 $[61, 61, -2w^{2} + w + 8]$ $-e^{3} + 2e^{2} + 4e - 6$
73 $[73, 73, -w^{3} + 5w - 1]$ $\phantom{-}2e^{3} - e^{2} - 14e + 1$
79 $[79, 79, 2w^{2} + w - 6]$ $-2e^{3} + 2e^{2} + 10e + 2$
79 $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ $-e^{3} + e^{2} + 3e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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