Properties

Label 4.4.13025.1-20.1-d
Base field 4.4.13025.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20, 10, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{11}{2}]$
Dimension $4$
CM no
Base change no

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Base field 4.4.13025.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 3x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[20, 10, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{11}{2}]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 4x^{3} - 8x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + w + 8]$ $-1$
5 $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $\phantom{-}1$
5 $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ $-e^{2} - 2e + 1$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $-e^{2} - 4e - 1$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ $\phantom{-}e^{3} + 3e^{2} - e - 5$
29 $[29, 29, w]$ $-2e^{3} - 6e^{2} + 4e + 10$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ $\phantom{-}2e^{2} + 4e - 4$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ $\phantom{-}2e^{3} + 5e^{2} - 8e - 11$
29 $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ $-2e^{3} - 6e^{2} + 6e + 12$
41 $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ $-e^{3} - 2e^{2} + 5e - 2$
41 $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ $\phantom{-}e^{3} + 3e^{2} + e - 3$
61 $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ $\phantom{-}3e^{3} + 9e^{2} - 11e - 17$
61 $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ $-3e^{3} - 8e^{2} + 11e + 12$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ $-2e^{3} - 7e^{2} + 2e + 3$
79 $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ $\phantom{-}2e^{3} + 8e^{2} - 4e - 14$
81 $[81, 3, -3]$ $\phantom{-}2e^{3} + 7e^{2} - 4e - 13$
89 $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ $-e^{3} + 9e - 8$
89 $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ $-e^{3} - 3e^{2} + 3e + 3$
109 $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ $\phantom{-}2e^{3} + 6e^{2} - 8e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + w + 8]$ $1$
$5$ $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $-1$