Properties

Label 4.4.9301.1-17.1-a
Base field 4.4.9301.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{3} + w^{2} + 4w - 2]$
Dimension $2$
CM no
Base change no

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Base field 4.4.9301.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, -w^{3} + w^{2} + 4w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $13$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + 2x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
5 $[5, 5, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2]$ $-2$
7 $[7, 7, -w^{2} + w + 2]$ $\phantom{-}e + 4$
16 $[16, 2, 2]$ $\phantom{-}5$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $-1$
23 $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e - 2$
27 $[27, 3, -w^{3} + w^{2} + 5w - 1]$ $\phantom{-}2e + 4$
37 $[37, 37, -w^{3} + 4w + 1]$ $\phantom{-}6$
37 $[37, 37, -w^{3} + w^{2} + 2w + 1]$ $\phantom{-}2$
49 $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ $\phantom{-}3e + 2$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}2e + 10$
61 $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ $-4e$
67 $[67, 67, w^{2} - 3w - 2]$ $-2e - 2$
71 $[71, 71, -w^{2} + 5]$ $\phantom{-}4e + 8$
71 $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ $-2e - 6$
71 $[71, 71, w^{2} - 2w - 5]$ $\phantom{-}4$
79 $[79, 79, w^{2} - 3w - 1]$ $-2e - 14$
79 $[79, 79, w^{3} - 6w - 1]$ $-e + 2$
89 $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ $\phantom{-}3e + 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $1$