Properties

Label 3.3.1944.1-8.4-a
Base field 3.3.1944.1
Weight $[2, 2, 2]$
Level norm $8$
Level $[8, 8, 4w^{2} - 3w - 34]$
Dimension $6$
CM no
Base change no

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Base field 3.3.1944.1

Generator \(w\), with minimal polynomial \(x^{3} - 9x - 6\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[8, 8, 4w^{2} - 3w - 34]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{6} + x^{5} - 7x^{4} - 7x^{3} + 6x^{2} + 6x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + 2w + 2]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 9]$ $-2e^{5} - e^{4} + 14e^{3} + 7e^{2} - 13e - 5$
7 $[7, 7, w^{2} - w - 7]$ $\phantom{-}2e^{5} + e^{4} - 15e^{3} - 7e^{2} + 18e + 5$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}e^{3} - 5e - 2$
13 $[13, 13, -2w - 1]$ $\phantom{-}e^{5} + e^{4} - 8e^{3} - 8e^{2} + 12e + 8$
17 $[17, 17, -2w^{2} + 6w + 5]$ $\phantom{-}e^{5} - 7e^{3} + 6e + 1$
31 $[31, 31, -2w^{2} + 2w + 19]$ $-e^{5} + 8e^{3} + e^{2} - 12e - 7$
37 $[37, 37, 2w^{2} - 13]$ $\phantom{-}3e^{5} + 3e^{4} - 21e^{3} - 19e^{2} + 20e + 8$
41 $[41, 41, w^{2} - w - 5]$ $-3e^{5} - 2e^{4} + 20e^{3} + 14e^{2} - 16e - 9$
43 $[43, 43, 2w^{2} - 2w - 17]$ $-3e^{5} - e^{4} + 21e^{3} + 9e^{2} - 21e - 13$
43 $[43, 43, -2w + 7]$ $\phantom{-}e^{5} - 6e^{3} - e^{2} - e + 1$
43 $[43, 43, 12w^{2} - 8w - 101]$ $-6e^{5} - 5e^{4} + 43e^{3} + 32e^{2} - 42e - 18$
49 $[49, 7, w^{2} + w - 1]$ $-4e^{5} + 30e^{3} + e^{2} - 37e - 3$
59 $[59, 59, -w^{2} + w + 11]$ $\phantom{-}9e^{5} + 6e^{4} - 64e^{3} - 40e^{2} + 61e + 28$
61 $[61, 61, -w^{2} - w - 1]$ $\phantom{-}3e^{5} - 20e^{3} + e^{2} + 12e - 4$
79 $[79, 79, -2w^{2} + 4w + 7]$ $-5e^{5} - 6e^{4} + 36e^{3} + 38e^{2} - 36e - 22$
83 $[83, 83, 2w - 1]$ $\phantom{-}5e^{5} + 6e^{4} - 36e^{3} - 41e^{2} + 33e + 22$
89 $[89, 89, 5w^{2} - 3w - 43]$ $\phantom{-}2e^{4} - e^{3} - 17e^{2} + 6e + 14$
103 $[103, 103, -2w + 5]$ $-14e^{5} - 8e^{4} + 101e^{3} + 53e^{2} - 101e - 39$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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