Properties

Base field 4.4.8768.1
Weight [2, 2, 2, 2]
Level norm 1
Level $[1, 1, 1]$
Label 4.4.8768.1-1.1-a
Dimension 3
CM no
Base change yes

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Base field 4.4.8768.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[1, 1, 1]$
Label 4.4.8768.1-1.1-a
Dimension 3
Is CM no
Is base change yes
Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut 5x^{2} \) \(\mathstrut +\mathstrut x \) \(\mathstrut +\mathstrut 14\)

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Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
7 $[7, 7, w]$ $\phantom{-}e^{2} - 3e - 2$
7 $[7, 7, -w^{2} + 2w + 1]$ $-e^{2} + 2e + 4$
7 $[7, 7, w^{2} - 2]$ $-e^{2} + 2e + 4$
7 $[7, 7, w - 1]$ $\phantom{-}e^{2} - 3e - 2$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $-3e^{2} + 6e + 12$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $-3e^{2} + 6e + 12$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}3e^{2} - 5e - 18$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}3e^{2} - 5e - 18$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}3e^{2} - 3e - 18$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}3e^{2} - 3e - 18$
47 $[47, 47, w^{2} - 2w - 5]$ $-3e + 6$
47 $[47, 47, w^{2} - 6]$ $-3e + 6$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-3e^{2} + 3e + 18$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-3e^{2} + 3e + 18$
79 $[79, 79, -w - 3]$ $\phantom{-}3e^{2} - 8e - 12$
79 $[79, 79, w - 4]$ $\phantom{-}3e^{2} - 8e - 12$
81 $[81, 3, -3]$ $-3e^{2} + 3e + 28$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}3e^{2} - 6e - 12$
89 $[89, 89, w^{2} + w - 4]$ $\phantom{-}3e^{2} - 6e - 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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