Properties

Label 4.4.13025.1-1.1-a
Base field 4.4.13025.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $5$
CM no
Base change yes

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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: $[1, 1, 1]$
Dimension: $5$
CM: no
Base change: yes
Newspace dimension: $5$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} + x^{4} - 14x^{3} - 14x^{2} + 33x + 25\)

  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 $[4, 2, -w^{2} + w + 8]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $-\frac{1}{4}e^{4} + 3e^{2} - \frac{19}{4}$
5 $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ $-\frac{1}{4}e^{4} + 3e^{2} - \frac{19}{4}$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $\phantom{-}e^{2} - 5$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ $\phantom{-}e^{2} - 5$
29 $[29, 29, w]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{5}{2}$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{7}{2}e^{2} + \frac{7}{2}e + \frac{25}{4}$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{5}{2}$
29 $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{7}{2}e^{2} + \frac{7}{2}e + \frac{25}{4}$
41 $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{11}{2}e^{2} - \frac{9}{2}e - 7$
41 $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{11}{2}e^{2} - \frac{9}{2}e - 7$
61 $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{7}{2}e^{2} + \frac{7}{2}e - \frac{33}{4}$
61 $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{7}{2}e^{2} + \frac{7}{2}e - \frac{33}{4}$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 6e^{2} + 7e + \frac{15}{2}$
79 $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ $\phantom{-}\frac{1}{2}e^{4} - e^{3} - 6e^{2} + 7e + \frac{15}{2}$
81 $[81, 3, -3]$ $-e^{3} - e^{2} + 7e + 13$
89 $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{11}{2}e + \frac{45}{4}$
89 $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{11}{2}e + \frac{45}{4}$
109 $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{15}{2}e^{2} + \frac{13}{2}e + 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).