Properties

Label 4.4.12725.1-25.1-j
Base field 4.4.12725.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -2w^{2} + 2w + 11]$
Dimension $17$
CM no
Base change yes

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Base field 4.4.12725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -2w^{2} + 2w + 11]$
Dimension: $17$
CM: no
Base change: yes
Newspace dimension: $29$

Hecke eigenvalues ($q$-expansion)

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

\(x^{17} - 2x^{16} - 99x^{15} + 164x^{14} + 4012x^{13} - 5417x^{12} - 85844x^{11} + 92652x^{10} + 1044708x^{9} - 879559x^{8} - 7281096x^{7} + 4652445x^{6} + 27964035x^{5} - 13472926x^{4} - 53814081x^{3} + 20542611x^{2} + 39433176x - 14511992\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $...$
11 $[11, 11, w^{2} - 5]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}e$
11 $[11, 11, w - 2]$ $...$
16 $[16, 2, 2]$ $...$
19 $[19, 19, w^{2} - 2w - 5]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
25 $[25, 5, -2w^{2} + 2w + 11]$ $-1$
29 $[29, 29, w]$ $...$
29 $[29, 29, 2w^{2} - w - 10]$ $...$
29 $[29, 29, -2w^{2} + 3w + 9]$ $...$
29 $[29, 29, w - 1]$ $...$
31 $[31, 31, w^{3} - 6w - 6]$ $...$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $...$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $...$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $...$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $...$
59 $[59, 59, 2w^{2} - w - 13]$ $...$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $...$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, -2w^{2} + 2w + 11]$ $1$