Properties

Label 4.4.4400.1-29.1-a
Base field 4.4.4400.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, w^{3} - 2w^{2} - 3w + 7]$
Dimension $6$
CM no
Base change no

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Base field 4.4.4400.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[29, 29, w^{3} - 2w^{2} - 3w + 7]$
Dimension: $6$
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:

\(x^{6} - 15x^{4} + 32x^{2} - 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $-\frac{3}{8}e^{5} + \frac{41}{8}e^{3} - \frac{9}{2}e$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{15}{4}e^{3} + 7e$
11 $[11, 11, w]$ $-\frac{5}{8}e^{5} + \frac{71}{8}e^{3} - \frac{25}{2}e$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $-1$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $\phantom{-}e^{4} - 14e^{2} + 18$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $-\frac{3}{8}e^{5} + \frac{41}{8}e^{3} - \frac{15}{2}e$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $\phantom{-}\frac{3}{4}e^{5} - \frac{41}{4}e^{3} + 11e$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $\phantom{-}\frac{3}{4}e^{5} - \frac{41}{4}e^{3} + 11e$
41 $[41, 41, w^{3} - 5w + 2]$ $\phantom{-}\frac{3}{4}e^{5} - \frac{41}{4}e^{3} + 11e$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{19}{4}e^{3} + 17e$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{41}{2}e^{3} + 24e$
59 $[59, 59, -3w^{2} - w + 10]$ $\phantom{-}2e^{4} - 27e^{2} + 28$
59 $[59, 59, -3w^{2} + w + 10]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{15}{2}e^{2} + 20$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $\phantom{-}\frac{3}{8}e^{5} - \frac{41}{8}e^{3} + \frac{9}{2}e$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $-\frac{3}{2}e^{5} + \frac{41}{2}e^{3} - 22e$
71 $[71, 71, 2w^{2} + w - 9]$ $\phantom{-}\frac{3}{2}e^{4} - \frac{43}{2}e^{2} + 28$
71 $[71, 71, 2w^{2} - w - 9]$ $\phantom{-}2e^{2} - 12$
81 $[81, 3, -3]$ $\phantom{-}e^{4} - 15e^{2} + 18$
101 $[101, 101, 2w^{2} - w - 10]$ $\phantom{-}e^{4} - 12e^{2} + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $1$