Properties

Label 4.4.7600.1-29.1-d
Base field 4.4.7600.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, -w^{3} + 4w + 2]$
Dimension $8$
CM no
Base change no

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Base field 4.4.7600.1

Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[29, 29, -w^{3} + 4w + 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 19x^{6} + 115x^{4} - 233x^{2} + 128\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{3} + w^{2} + 5w - 6]$ $\phantom{-}e$
9 $[9, 3, -w^{2} - w + 4]$ $-\frac{1}{8}e^{7} + \frac{13}{8}e^{5} - \frac{47}{8}e^{3} + \frac{59}{8}e$
9 $[9, 3, w^{2} - w - 4]$ $\phantom{-}\frac{1}{4}e^{5} - 3e^{3} + \frac{31}{4}e$
11 $[11, 11, w + 1]$ $-\frac{1}{8}e^{7} + \frac{17}{8}e^{5} - \frac{83}{8}e^{3} + \frac{99}{8}e$
11 $[11, 11, w - 1]$ $-\frac{1}{2}e^{3} + \frac{5}{2}e$
19 $[19, 19, -w]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e$
19 $[19, 19, -w^{2} - w + 6]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{17}{4}e^{2}$
19 $[19, 19, -w^{2} + w + 6]$ $\phantom{-}\frac{1}{4}e^{6} - 4e^{4} + \frac{75}{4}e^{2} - 18$
25 $[25, 5, 2w^{2} - 9]$ $-\frac{1}{4}e^{6} + 3e^{4} - \frac{31}{4}e^{2} + 2$
29 $[29, 29, -w^{3} + 4w + 2]$ $-1$
29 $[29, 29, -w^{3} + 4w - 2]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{9}{2}e^{4} + \frac{93}{4}e^{2} - 26$
41 $[41, 41, 2w^{2} - w - 7]$ $\phantom{-}e^{5} - 10e^{3} + 17e$
41 $[41, 41, w^{3} - w^{2} - 6w + 4]$ $\phantom{-}e^{5} - 10e^{3} + 17e$
61 $[61, 61, -w^{3} + 3w^{2} + 6w - 14]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{9}{2}e^{5} + \frac{93}{4}e^{3} - 28e$
61 $[61, 61, w^{3} + 2w^{2} - 5w - 8]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{5}{2}e^{3} + \frac{13}{4}e$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 8]$ $-\frac{1}{2}e^{5} + 5e^{3} - \frac{9}{2}e$
61 $[61, 61, w^{3} + 3w^{2} - 6w - 14]$ $-\frac{1}{8}e^{7} + \frac{19}{8}e^{5} - \frac{107}{8}e^{3} + \frac{145}{8}e$
89 $[89, 89, -w^{3} + w^{2} + 6w - 9]$ $\phantom{-}\frac{1}{4}e^{6} - 4e^{4} + \frac{75}{4}e^{2} - 22$
89 $[89, 89, 2w^{3} - w^{2} - 10w + 10]$ $-\frac{1}{4}e^{6} + e^{4} + \frac{33}{4}e^{2} - 6$
109 $[109, 109, -w^{3} + 5w^{2} + 7w - 23]$ $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{17}{4}e^{3} + e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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