Properties

Label 4.4.7053.1-17.1-b
Base field 4.4.7053.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, -w^{3} + 2w^{2} + 2w - 2]$
Dimension $2$
CM no
Base change no

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Base field 4.4.7053.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, -w^{3} + 2w^{2} + 2w - 2]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
7 $[7, 7, w^{2} - w - 2]$ $-e - 2$
9 $[9, 3, w^{2} - 2w - 1]$ $\phantom{-}e - 1$
13 $[13, 13, w^{3} - 3w^{2} - w + 5]$ $-4e - 2$
13 $[13, 13, w^{3} - 3w^{2} - w + 2]$ $-4e - 2$
16 $[16, 2, 2]$ $-2e - 3$
17 $[17, 17, -w^{3} + 2w^{2} + 2w - 2]$ $-1$
19 $[19, 19, -w^{3} + 2w^{2} + 2w - 1]$ $\phantom{-}3e + 5$
29 $[29, 29, -2w^{3} + 5w^{2} + 4w - 7]$ $\phantom{-}5e + 4$
31 $[31, 31, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}6e$
47 $[47, 47, -w^{3} + 4w^{2} - w - 5]$ $-5e - 4$
53 $[53, 53, -w^{3} + 4w^{2} - w - 7]$ $-5e + 1$
67 $[67, 67, 2w^{3} - 3w^{2} - 8w + 1]$ $\phantom{-}3e - 4$
67 $[67, 67, 2w^{3} - 5w^{2} - 4w + 4]$ $-3e + 6$
71 $[71, 71, w^{3} - 3w^{2} - 2w + 2]$ $\phantom{-}2e$
79 $[79, 79, w^{2} - 3w - 4]$ $\phantom{-}11e + 3$
83 $[83, 83, 2w^{2} - 3w - 4]$ $\phantom{-}10$
89 $[89, 89, -3w^{3} + 7w^{2} + 8w - 11]$ $-4$
101 $[101, 101, w^{3} - 2w^{2} - 3w - 2]$ $\phantom{-}2e + 4$
103 $[103, 103, -2w^{3} + 4w^{2} + 5w - 1]$ $\phantom{-}e + 13$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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