Properties

Base field 4.4.9248.1
Weight [2, 2, 2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 4.4.9248.1-1.1-a
Dimension 6
CM no
Base change yes

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Base field 4.4.9248.1

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 2\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[1, 1, 1]$
Label 4.4.9248.1-1.1-a
Dimension 6
Is CM no
Is base change yes
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 11x^{4} \) \(\mathstrut +\mathstrut 26x^{2} \) \(\mathstrut -\mathstrut 8\)

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Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{11}{4}e^{3} + \frac{11}{2}e$
13 $[13, 13, -w^{2} + w + 3]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 6e$
13 $[13, 13, w^{2} + w - 3]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 6e$
19 $[19, 19, -w^{3} + 3w + 1]$ $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 13e$
19 $[19, 19, -w^{3} + 3w - 1]$ $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 13e$
43 $[43, 43, -w^{2} + w - 1]$ $-e^{4} + 7e^{2} - 2$
43 $[43, 43, w^{2} + w + 1]$ $-e^{4} + 7e^{2} - 2$
49 $[49, 7, w^{3} + w^{2} - 6w - 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$
49 $[49, 7, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$
53 $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ $-e^{4} + 9e^{2} - 10$
53 $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ $-e^{4} + 9e^{2} - 10$
59 $[59, 59, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e^{4} - 11e^{2} + 14$
59 $[59, 59, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}e^{4} - 11e^{2} + 14$
67 $[67, 67, 3w^{3} - 13w + 1]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{29}{2}e^{3} + 21e$
67 $[67, 67, -w^{3} + w^{2} + 6w - 5]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{29}{2}e^{3} + 21e$
81 $[81, 3, -3]$ $\phantom{-}e^{4} - 9e^{2} + 18$
83 $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ $\phantom{-}e^{4} - 7e^{2} + 2$
83 $[83, 83, 4w^{3} - 18w - 1]$ $\phantom{-}e^{4} - 7e^{2} + 2$
89 $[89, 89, -2w^{3} + 10w + 1]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 2e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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