Properties

Base field 3.3.1101.1
Weight [2, 2, 2]
Level norm 8
Level $[8, 8, -w^{2} + 8]$
Label 3.3.1101.1-8.2-b
Dimension 4
CM no
Base change no

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Base field 3.3.1101.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[8, 8, -w^{2} + 8]$
Label 3.3.1101.1-8.2-b
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut -\mathstrut 6x^{2} \) \(\mathstrut +\mathstrut 4x \) \(\mathstrut +\mathstrut 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}0$
3 $[3, 3, -w + 3]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 2e + 2$
4 $[4, 2, w^{2} + w - 7]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 2e + 3$
19 $[19, 19, w + 1]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 5e$
23 $[23, 23, w^{2} - 2w - 1]$ $-\frac{3}{2}e^{3} - \frac{1}{2}e^{2} + 9e$
31 $[31, 31, -2w^{2} + 19]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 4e + 8$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}2e^{3} - e^{2} - 9e + 2$
31 $[31, 31, -3w + 5]$ $\phantom{-}2e^{3} - 2e^{2} - 10e + 6$
41 $[41, 41, w^{2} + 2w - 7]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 12$
43 $[43, 43, w^{2} - 11]$ $\phantom{-}3e^{2} - 2e - 6$
47 $[47, 47, 3w - 7]$ $\phantom{-}2e^{3} + e^{2} - 10e - 4$
53 $[53, 53, -3w^{2} - 6w + 11]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 5e - 4$
59 $[59, 59, 2w - 1]$ $\phantom{-}e^{3} - e^{2} - 3e$
67 $[67, 67, 2w^{2} + w - 19]$ $-e^{3} - e^{2} + 3e + 4$
67 $[67, 67, 3w^{2} + 2w - 25]$ $\phantom{-}3e^{3} - e^{2} - 16e + 2$
67 $[67, 67, w - 5]$ $-2e^{3} - 2e^{2} + 8e + 12$
73 $[73, 73, -4w^{2} - 3w + 29]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{7}{2}e^{2} - 5e + 12$
73 $[73, 73, 2w^{2} - w - 11]$ $\phantom{-}e^{3} + 3e^{2} - 4e - 8$
73 $[73, 73, w^{2} + 2w - 11]$ $-e^{3} + 4e^{2} + 5e - 10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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