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 4.4.18432.1-7.4-e
Dimension 8
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 4.4.18432.1-7.4-e
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 14

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 13x^{6} \) \(\mathstrut +\mathstrut 54x^{4} \) \(\mathstrut -\mathstrut 71x^{2} \) \(\mathstrut +\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $-\frac{1}{2}e^{6} + 5e^{4} - 12e^{2} + \frac{5}{2}$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{1}{2}e^{6} + 4e^{4} - 8e^{2} + \frac{9}{2}$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $\phantom{-}e^{2} - 3$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $-1$
9 $[9, 3, w - 3]$ $-\frac{1}{2}e^{7} + 7e^{5} - 31e^{3} + \frac{87}{2}e$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-\frac{1}{2}e^{7} + 8e^{5} - 38e^{3} + \frac{105}{2}e$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $-\frac{3}{2}e^{7} + 17e^{5} - 60e^{3} + \frac{131}{2}e$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $\phantom{-}\frac{3}{2}e^{7} - 20e^{5} + 84e^{3} - \frac{215}{2}e$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $-e^{7} + 12e^{5} - 47e^{3} + 60e$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}e^{7} - 13e^{5} + 54e^{3} - 70e$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $\phantom{-}2e^{5} - 16e^{3} + 26e$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-\frac{1}{2}e^{7} + 8e^{5} - 42e^{3} + \frac{141}{2}e$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}4e^{5} - 33e^{3} + 63e$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $\phantom{-}2e^{7} - 25e^{5} + 100e^{3} - 129e$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}2e^{7} - 23e^{5} + 83e^{3} - 92e$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $\phantom{-}\frac{1}{2}e^{7} - 2e^{5} - 13e^{3} + \frac{97}{2}e$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-3e^{7} + 34e^{5} - 118e^{3} + 121e$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $-e^{4} + 8e^{2} - 11$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $\phantom{-}e^{6} - 9e^{4} + 17e^{2} + 15$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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