Properties

Label 4.4.16317.1-1.1-c
Base field 4.4.16317.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $2$
CM yes
Base change yes

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Base field 4.4.16317.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $2$
CM: yes
Base change: yes
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}0$
5 $[5, 5, -w + 2]$ $\phantom{-}0$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $\phantom{-}e - 1$
16 $[16, 2, 2]$ $\phantom{-}8$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}0$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}0$
25 $[25, 5, w^{2} - w - 3]$ $-3e - 4$
37 $[37, 37, 2w - 1]$ $\phantom{-}4e + 6$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $\phantom{-}e + 9$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}e + 9$
59 $[59, 59, 2w - 5]$ $\phantom{-}0$
59 $[59, 59, -2w - 3]$ $\phantom{-}0$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $-3e - 13$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $-3e - 13$
83 $[83, 83, -w^{3} + 7w]$ $\phantom{-}0$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}0$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}0$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).