Properties

Base field 3.3.1129.1
Weight [2, 2, 2]
Level norm 19
Level $[19, 19, -w^{2} - w + 4]$
Label 3.3.1129.1-19.1-c
Dimension 8
CM no
Base change no

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Base field 3.3.1129.1

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

Form

Weight [2, 2, 2]
Level $[19, 19, -w^{2} - w + 4]$
Label 3.3.1129.1-19.1-c
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 36

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 10x^{6} \) \(\mathstrut +\mathstrut 24x^{4} \) \(\mathstrut -\mathstrut 18x^{2} \) \(\mathstrut +\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-e^{6} + 9e^{4} - 15e^{2} + 4$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e^{7} - 8e^{5} + 7e^{3} + 4e$
8 $[8, 2, 2]$ $\phantom{-}e^{6} - 9e^{4} + 15e^{2} - 5$
11 $[11, 11, -w^{2} + 5]$ $-3e^{7} + 26e^{5} - 38e^{3} + 9e$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}3e^{7} - 27e^{5} + 46e^{3} - 17e$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}e^{3} - 6e$
19 $[19, 19, -w^{2} - w + 4]$ $-1$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-e^{7} + 10e^{5} - 24e^{3} + 18e$
31 $[31, 31, w^{2} - 2w - 4]$ $-3e^{7} + 25e^{5} - 30e^{3} - e$
37 $[37, 37, -2w^{2} + 3w + 7]$ $\phantom{-}e^{7} - 11e^{5} + 33e^{3} - 33e$
41 $[41, 41, w^{2} - 2]$ $-2e^{7} + 16e^{5} - 16e^{3}$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}7e^{6} - 61e^{4} + 90e^{2} - 18$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}e^{4} - 5e^{2} - 2$
67 $[67, 67, 2w^{2} - w - 11]$ $\phantom{-}2e^{7} - 17e^{5} + 23e^{3} - 3e$
73 $[73, 73, -w^{2} - 1]$ $-3e^{6} + 25e^{4} - 30e^{2}$
83 $[83, 83, w^{2} - w - 10]$ $-8e^{6} + 68e^{4} - 91e^{2} + 6$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}e^{6} - 8e^{4} + 4e^{2} + 14$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}4e^{7} - 37e^{5} + 69e^{3} - 31e$
97 $[97, 97, -w^{2} - 4w - 5]$ $\phantom{-}4e^{6} - 34e^{4} + 46e^{2} - 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} - w + 4]$ $1$