Properties

Label 4.4.15125.1-1.1-c
Base field 4.4.15125.1
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 4.4.15125.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 14x^{2} + 14x + 31\); narrow class number \(4\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $2$
CM: yes
Base change: yes
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 44\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, 4w^{3} + 7w^{2} - 37w - 45]$ $\phantom{-}0$
11 $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ $-e$
11 $[11, 11, -w + 2]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}3$
19 $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ $\phantom{-}0$
19 $[19, 19, -w^{3} - w^{2} + 9w + 3]$ $\phantom{-}0$
19 $[19, 19, -2w^{3} - 4w^{2} + 17w + 23]$ $\phantom{-}0$
19 $[19, 19, w^{3} + 2w^{2} - 10w - 10]$ $\phantom{-}0$
29 $[29, 29, -w - 2]$ $\phantom{-}0$
29 $[29, 29, -w^{3} - 2w^{2} + 8w + 15]$ $\phantom{-}0$
29 $[29, 29, 2w^{3} + 3w^{2} - 18w - 20]$ $\phantom{-}0$
29 $[29, 29, -3w^{3} - 5w^{2} + 27w + 28]$ $\phantom{-}0$
31 $[31, 31, 3w^{3} + 5w^{2} - 27w - 31]$ $-e$
31 $[31, 31, -3w^{3} - 5w^{2} + 27w + 30]$ $\phantom{-}e$
31 $[31, 31, -2w^{3} - 3w^{2} + 18w + 17]$ $-e$
31 $[31, 31, 2w^{3} + 3w^{2} - 18w - 18]$ $\phantom{-}e$
71 $[71, 71, -w^{3} - 2w^{2} + 10w + 8]$ $\phantom{-}8$
71 $[71, 71, 4w^{3} + 8w^{2} - 35w - 50]$ $\phantom{-}8$
71 $[71, 71, -4w^{3} - 7w^{2} + 36w + 47]$ $\phantom{-}8$
71 $[71, 71, -w^{3} - 2w^{2} + 8w + 17]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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