Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 4.4.18688.1-1.1-b
Dimension 8
CM no
Base change yes

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Base field 4.4.18688.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[1, 1, 1]$
Label 4.4.18688.1-1.1-b
Dimension 8
Is CM no
Is base change yes
Parent newspace dimension 9

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 19x^{6} \) \(\mathstrut +\mathstrut 124x^{4} \) \(\mathstrut -\mathstrut 320x^{2} \) \(\mathstrut +\mathstrut 272\)

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Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $-\frac{1}{4}e^{7} + \frac{15}{4}e^{5} - 17e^{3} + 22e$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $-\frac{1}{4}e^{7} + \frac{15}{4}e^{5} - 17e^{3} + 22e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}e^{4} - 10e^{2} + 19$
9 $[9, 3, w + 1]$ $\phantom{-}e^{4} - 10e^{2} + 19$
17 $[17, 17, w + 3]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{15}{2}e^{4} + 34e^{2} - 45$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{15}{2}e^{4} + 34e^{2} - 45$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{19}{4}e^{5} + 27e^{3} - 42e$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{19}{4}e^{5} + 27e^{3} - 42e$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $\phantom{-}e^{6} - 14e^{4} + 56e^{2} - 57$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}e^{6} - 14e^{4} + 56e^{2} - 57$
41 $[41, 41, 2w + 3]$ $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 24e^{2} + 23$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 24e^{2} + 23$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $-\frac{1}{4}e^{7} + \frac{11}{4}e^{5} - 7e^{3} + 2e$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-\frac{1}{4}e^{7} + \frac{11}{4}e^{5} - 7e^{3} + 2e$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 24e^{2} + 31$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{17}{2}e^{4} + 42e^{2} - 53$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $\phantom{-}\frac{1}{2}e^{6} - \frac{17}{2}e^{4} + 42e^{2} - 53$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $\phantom{-}e^{6} - 13e^{4} + 52e^{2} - 70$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{11}{4}e^{5} + 9e^{3} - 18e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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