Properties

Base field 4.4.18432.1
Weight [2, 2, 2, 2]
Level norm 4
Level $[4, 2, \frac{1}{3}w^{2} - 2]$
Label 4.4.18432.1-4.1-a
Dimension 4
CM yes
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 $[4, 2, \frac{1}{3}w^{2} - 2]$
Label 4.4.18432.1-4.1-a
Dimension 4
Is CM yes
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut 8x^{3} \) \(\mathstrut -\mathstrut 4x^{2} \) \(\mathstrut -\mathstrut 128x \) \(\mathstrut -\mathstrut 164\)

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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 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{3}{2}e^{3} - 4e^{2} + 28e + 42$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 10e - 12$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}e^{3} + 3e^{2} - 19e - 38$
9 $[9, 3, w - 3]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}0$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}0$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $\phantom{-}0$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}0$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}0$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $\phantom{-}0$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}0$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $\phantom{-}0$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $\phantom{-}0$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}6e^{3} + 17e^{2} - 110e - 186$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-3e^{3} - 9e^{2} + 52e + 102$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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