Properties

Base field 4.4.18432.1
Weight [2, 2, 2, 2]
Level norm 8
Level $[8, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 2]$
Label 4.4.18432.1-8.1-a
Dimension 4
CM no
Base change no

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Base field 4.4.18432.1

Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[8, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 2]$
Label 4.4.18432.1-8.1-a
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 12x^{2} \) \(\mathstrut -\mathstrut 16x \) \(\mathstrut -\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}0$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{1}{2}e^{3} + 6e + 6$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $-\frac{1}{2}e^{3} + e^{2} + 4e$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}e^{3} - e^{2} - 11e - 6$
9 $[9, 3, w - 3]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}e^{3} + e^{2} - 14e - 14$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}e^{3} - e^{2} - 14e - 2$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $-3e^{3} + 3e^{2} + 34e + 22$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}e^{3} - 3e^{2} - 6e + 10$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}e^{3} - 2e^{2} - 6e + 4$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $-e^{3} + 10e + 16$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-3e^{3} + 4e^{2} + 30e + 16$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}3e^{3} - 2e^{2} - 34e - 20$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $-2e^{3} + 4e^{2} + 16e$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}4e$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $\phantom{-}4e^{3} - 4e^{2} - 44e - 24$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-2e^{3} + 24e + 24$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $-2e^{3} + 3e^{2} + 22e + 2$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $\phantom{-}e^{3} + e^{2} - 16e - 22$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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