Properties

Label 4.4.5125.1-29.1-d
Base field 4.4.5125.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, w^{3} - 4w^{2} - w + 10]$
Dimension $2$
CM no
Base change no

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Base field 4.4.5125.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 7x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[29, 29, w^{3} - 4w^{2} - w + 10]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 2w + 3]$ $\phantom{-}e$
9 $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ $-\frac{3}{2}e - 3$
9 $[9, 3, -w^{3} + 5w + 5]$ $\phantom{-}\frac{3}{2}e$
11 $[11, 11, w]$ $\phantom{-}\frac{1}{2}e + 1$
11 $[11, 11, w - 1]$ $\phantom{-}\frac{1}{2}e - 2$
16 $[16, 2, 2]$ $-e - 3$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $-6$
19 $[19, 19, w^{3} - w^{2} - 4w + 2]$ $-\frac{3}{2}e$
29 $[29, 29, w^{3} - 4w^{2} - w + 10]$ $\phantom{-}1$
29 $[29, 29, -w^{3} + 3w^{2} + w - 7]$ $-\frac{3}{2}e + 3$
41 $[41, 41, 3w^{2} - 2w - 10]$ $-2e - 2$
49 $[49, 7, -2w^{2} + 3w + 8]$ $-\frac{3}{2}e$
49 $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ $-6$
71 $[71, 71, -w - 3]$ $\phantom{-}\frac{5}{2}e + 8$
71 $[71, 71, w - 4]$ $-2e - 4$
79 $[79, 79, -w^{3} + w^{2} + 3w + 3]$ $\phantom{-}\frac{3}{2}e - 9$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $-\frac{3}{2}e - 3$
89 $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ $-\frac{3}{2}e - 6$
89 $[89, 89, w^{3} - 6w - 2]$ $-3e - 12$
101 $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ $-e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w^{3} - 4w^{2} - w + 10]$ $-1$