Properties

Label 4.4.6809.1-17.1-d
Base field 4.4.6809.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{3} - w^{2} + 5w + 4]$
Dimension $5$
CM no
Base change no

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Base field 4.4.6809.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, -w^{3} - w^{2} + 5w + 4]$
Dimension: $5$
CM: no
Base change: no
Newspace dimension: $11$

Hecke eigenvalues ($q$-expansion)

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

\(x^{5} - 3x^{4} - 7x^{3} + 22x^{2} + 9x - 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 4w]$ $-e^{2} + e + 4$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $-e^{4} + e^{3} + 8e^{2} - 4e - 13$
11 $[11, 11, w^{3} - 5w + 1]$ $\phantom{-}e^{4} - e^{3} - 8e^{2} + 5e + 15$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $-1$
23 $[23, 23, -w^{2} + 2]$ $-e^{3} + 5e + 4$
29 $[29, 29, -w^{2} - w + 3]$ $-e^{4} + e^{3} + 7e^{2} - 4e - 7$
31 $[31, 31, -w^{3} + 6w + 2]$ $-2e^{4} + 2e^{3} + 17e^{2} - 9e - 30$
43 $[43, 43, w^{3} - 6w]$ $-e^{2} - e + 4$
47 $[47, 47, 2w^{3} - 9w]$ $\phantom{-}2e^{4} - 2e^{3} - 15e^{2} + 6e + 25$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $\phantom{-}e^{4} - 8e^{2} - 3e + 12$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $\phantom{-}e^{3} - e^{2} - 6e - 2$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}e^{4} - e^{3} - 12e^{2} + 6e + 28$
59 $[59, 59, 3w^{3} - 15w - 5]$ $\phantom{-}e^{4} - e^{3} - 8e^{2} + 4e + 6$
71 $[71, 71, w^{3} - 3w - 3]$ $-3e^{4} + e^{3} + 28e^{2} - 2e - 58$
81 $[81, 3, -3]$ $\phantom{-}e^{4} - e^{3} - 5e^{2} + e + 2$
83 $[83, 83, -2w^{3} + 8w + 3]$ $\phantom{-}e^{4} - 12e^{2} + 2e + 33$
89 $[89, 89, -2w^{3} + 11w - 2]$ $\phantom{-}4e^{4} - 3e^{3} - 34e^{2} + 11e + 64$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $\phantom{-}2e^{3} - 7e^{2} - 8e + 27$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $-2e^{4} + 13e^{2} + 7e - 14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $1$