Properties

Base field 4.4.18432.1
Weight [2, 2, 2, 2]
Level norm 7
Level $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$
Label 4.4.18432.1-7.1-a
Dimension 1
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 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$
Label 4.4.18432.1-7.1-a
Dimension 1
Is CM no
Is base change no
Parent newspace dimension 14

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}1$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $-1$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $\phantom{-}5$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $\phantom{-}0$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}2$
9 $[9, 3, w - 3]$ $-2$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}3$
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 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}8$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $-8$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $-13$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}12$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}7$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $\phantom{-}6$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}6$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-9$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $\phantom{-}11$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}15$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $\phantom{-}6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $1$