Properties

Base field 3.3.316.1
Weight [2, 2, 2]
Level norm 17
Level $[17, 17, -w^{2} - w + 3]$
Label 3.3.316.1-17.1-b
Dimension 3
CM no
Base change no

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Base field 3.3.316.1

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

Form

Weight [2, 2, 2]
Level $[17, 17, -w^{2} - w + 3]$
Label 3.3.316.1-17.1-b
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 5

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut +\mathstrut 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}e^{2} + 2e - 3$
17 $[17, 17, -w^{2} - w + 3]$ $\phantom{-}1$
19 $[19, 19, w^{2} - w + 1]$ $\phantom{-}e^{2} - e - 2$
23 $[23, 23, 2w - 3]$ $-e^{2} + 1$
27 $[27, 3, 3]$ $-2e^{2} - 3e + 7$
29 $[29, 29, 2w + 1]$ $-e^{2} - 3e$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}e^{2} + e + 4$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-e^{2} + 4e + 3$
41 $[41, 41, 2w^{2} - 9]$ $-e - 3$
43 $[43, 43, w^{2} + w - 5]$ $-4e^{2} - 3e + 9$
43 $[43, 43, -3w^{2} + w + 15]$ $\phantom{-}3e^{2} + e - 2$
43 $[43, 43, -2w^{2} + 2w + 11]$ $-3e^{2} + 7$
53 $[53, 53, w^{2} - w - 7]$ $-4e^{2} - 6e + 12$
61 $[61, 61, 4w^{2} - 2w - 15]$ $\phantom{-}5e^{2} - 15$
67 $[67, 67, -5w^{2} + 3w + 23]$ $\phantom{-}e^{2} + e + 8$
73 $[73, 73, 2w^{2} - 3]$ $-2e^{2} + e + 9$
73 $[73, 73, -3w^{2} - w + 7]$ $-e^{2} - 4e - 1$
73 $[73, 73, -6w^{2} + 4w + 25]$ $-e^{2} + 6e + 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
17 $[17, 17, -w^{2} - w + 3]$ $-1$