Properties

Base field 4.4.15952.1
Weight [2, 2, 2, 2]
Level norm 8
Level $[8, 2, w^{3} - w^{2} - 5w + 3]$
Label 4.4.15952.1-8.1-b
Dimension 5
CM no
Base change no

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Base field 4.4.15952.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[8, 2, w^{3} - w^{2} - 5w + 3]$
Label 4.4.15952.1-8.1-b
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut +\mathstrut 4x^{4} \) \(\mathstrut -\mathstrut 3x^{3} \) \(\mathstrut -\mathstrut 22x^{2} \) \(\mathstrut -\mathstrut 19x \) \(\mathstrut -\mathstrut 4\)

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Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}0$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}e$
11 $[11, 11, -w^{3} + 5w + 1]$ $\phantom{-}2e^{4} + 7e^{3} - 10e^{2} - 39e - 16$
11 $[11, 11, -w + 2]$ $-2e^{4} - 6e^{3} + 11e^{2} + 32e + 12$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $-2e - 2$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-e^{3} - 2e^{2} + 7e + 6$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{4} - 4e^{3} + 4e^{2} + 22e + 10$
23 $[23, 23, w^{3} - 6w]$ $-2e^{4} - 6e^{3} + 12e^{2} + 32e + 8$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $\phantom{-}2e^{4} + 6e^{3} - 10e^{2} - 31e - 16$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $\phantom{-}2e^{4} + 6e^{3} - 12e^{2} - 32e - 14$
41 $[41, 41, 2w^{3} - 11w - 4]$ $-2e^{3} - 4e^{2} + 13e + 14$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $-2e^{4} - 6e^{3} + 12e^{2} + 32e + 6$
59 $[59, 59, 2w^{3} - 11w - 2]$ $\phantom{-}3e^{4} + 10e^{3} - 16e^{2} - 56e - 20$
67 $[67, 67, w^{3} - 7w - 1]$ $\phantom{-}e^{4} + 4e^{3} - 4e^{2} - 26e - 20$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $\phantom{-}0$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $\phantom{-}2e^{4} + 8e^{3} - 8e^{2} - 48e - 24$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $-2e^{4} - 5e^{3} + 12e^{2} + 25e + 6$
101 $[101, 101, -2w^{3} + 13w + 6]$ $-2e^{4} - 8e^{3} + 8e^{2} + 50e + 30$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $\phantom{-}4e^{4} + 14e^{3} - 20e^{2} - 82e - 34$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $\phantom{-}4e^{4} + 14e^{3} - 20e^{2} - 76e - 34$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-1$