Properties

Base field 4.4.18432.1
Weight [2, 2, 2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 4.4.18432.1-1.1-a
Dimension 4
CM no
Base change yes

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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 $[1, 1, 1]$
Label 4.4.18432.1-1.1-a
Dimension 4
Is CM no
Is base change yes
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut +\mathstrut 4x^{3} \) \(\mathstrut -\mathstrut 28x^{2} \) \(\mathstrut -\mathstrut 64x \) \(\mathstrut -\mathstrut 8\)

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Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{13}{5}e - \frac{14}{5}$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{18}{5}e - \frac{14}{5}$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{1}{10}e^{3} - \frac{3}{10}e^{2} + \frac{18}{5}e + \frac{24}{5}$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $-\frac{1}{10}e^{3} - \frac{3}{10}e^{2} + \frac{18}{5}e + \frac{24}{5}$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{18}{5}e - \frac{14}{5}$
9 $[9, 3, w - 3]$ $-\frac{1}{5}e^{3} - \frac{3}{5}e^{2} + \frac{26}{5}e + \frac{28}{5}$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-\frac{1}{10}e^{3} + \frac{1}{5}e^{2} + \frac{18}{5}e - \frac{26}{5}$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $-\frac{1}{10}e^{3} - \frac{4}{5}e^{2} + \frac{8}{5}e + \frac{54}{5}$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $-\frac{1}{10}e^{3} - \frac{4}{5}e^{2} + \frac{8}{5}e + \frac{54}{5}$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $-\frac{1}{10}e^{3} + \frac{1}{5}e^{2} + \frac{18}{5}e - \frac{26}{5}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{36}{5}e - \frac{48}{5}$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-\frac{1}{5}e^{3} - \frac{3}{5}e^{2} + \frac{36}{5}e + \frac{28}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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