Properties

Label 4.4.19025.1-1.1-b
Base field 4.4.19025.1
Weight $[2, 2, 2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $4$
CM no
Base change yes

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Base field 4.4.19025.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[1, 1, 1]$
Dimension: $4$
CM: no
Base change: yes
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 3x^{3} - 5x^{2} - 12x + 5\)

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Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $\phantom{-}e + 1$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $\phantom{-}e + 1$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $-e^{3} - 2e^{2} + 4e + 3$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $-e^{3} - 2e^{2} + 4e + 3$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $-e^{3} - e^{2} + 4e - 2$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $-e^{3} - e^{2} + 4e - 2$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $-e^{3} - e^{2} + 5e + 3$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $-e^{3} - e^{2} + 6e - 2$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $-e^{3} - e^{2} + 6e - 2$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $-e^{3} - e^{2} + 5e + 3$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $\phantom{-}2e^{2} + 4e - 8$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $\phantom{-}2e^{2} + 4e - 8$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $\phantom{-}e^{3} - e^{2} - 7e + 7$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $\phantom{-}e^{3} - e^{2} - 7e + 7$
81 $[81, 3, -3]$ $-3e^{2} - 5e + 18$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $\phantom{-}3e^{2} + 5e - 10$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $\phantom{-}e^{3} - 7e$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $\phantom{-}e^{3} - 7e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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