Properties

Label 3.3.1940.1-17.1-b
Base field 3.3.1940.1
Weight $[2, 2, 2]$
Level norm $17$
Level $[17, 17, -2w^{2} + 15]$
Dimension $6$
CM no
Base change no

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Base field 3.3.1940.1

Generator \(w\), with minimal polynomial \(x^{3} - 8x - 2\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[17, 17, -2w^{2} + 15]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $80$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 10x^{4} + 9x^{2} - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}1$
3 $[3, 3, w^{2} - 7]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $-4e^{5} + 38e^{3} - 17e$
5 $[5, 5, -w - 3]$ $-2e^{4} + 19e^{2} - 8$
9 $[9, 3, w^{2} - 2w - 1]$ $-2e^{5} + 19e^{3} - 9e$
17 $[17, 17, -2w^{2} + 15]$ $-1$
17 $[17, 17, 3w + 1]$ $\phantom{-}e^{3} - 9e$
17 $[17, 17, -w^{2} + w + 5]$ $\phantom{-}9e^{5} - 86e^{3} + 41e$
19 $[19, 19, -2w^{2} + w + 15]$ $\phantom{-}3e^{5} - 28e^{3} + 8e$
29 $[29, 29, w^{2} - w - 1]$ $\phantom{-}3e^{5} - 28e^{3} + 9e$
41 $[41, 41, w^{2} - 5]$ $-e^{5} + 9e^{3} - 2e$
43 $[43, 43, w^{2} + w - 3]$ $\phantom{-}4e^{5} - 39e^{3} + 25e$
47 $[47, 47, 2w - 1]$ $\phantom{-}3e^{4} - 28e^{2} + 4$
53 $[53, 53, -2w - 3]$ $-5e^{5} + 46e^{3} - 9e$
59 $[59, 59, w^{2} - w - 11]$ $\phantom{-}13e^{4} - 123e^{2} + 56$
71 $[71, 71, w^{2} - 3]$ $-6e^{5} + 56e^{3} - 21e$
73 $[73, 73, 6w^{2} - 2w - 47]$ $-3e^{5} + 28e^{3} - 6e$
83 $[83, 83, w^{2} - 4w + 1]$ $\phantom{-}10e^{4} - 95e^{2} + 42$
83 $[83, 83, 3w^{2} - 25]$ $\phantom{-}5e^{4} - 46e^{2} + 16$
83 $[83, 83, w - 5]$ $\phantom{-}11e^{4} - 107e^{2} + 52$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -2w^{2} + 15]$ $1$