Properties

Label 4.4.4913.1-17.1-a
Base field 4.4.4913.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, \frac{1}{2}w^{3} - w^{2} - w + \frac{3}{2}]$
Dimension $1$
CM no
Base change yes

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Base field 4.4.4913.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, \frac{1}{2}w^{3} - w^{2} - w + \frac{3}{2}]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $3$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + 3w + \frac{5}{2}]$ $-3$
4 $[4, 2, w^{3} - w^{2} - 6w]$ $-3$
13 $[13, 13, -\frac{1}{2}w^{3} + w^{2} + 3w - \frac{1}{2}]$ $-2$
13 $[13, 13, \frac{1}{2}w^{3} - w^{2} - 3w + \frac{7}{2}]$ $-2$
13 $[13, 13, -\frac{1}{2}w^{3} + 4w - \frac{1}{2}]$ $-2$
13 $[13, 13, -\frac{1}{2}w^{3} + 4w + \frac{5}{2}]$ $-2$
17 $[17, 17, \frac{1}{2}w^{3} - w^{2} - w + \frac{3}{2}]$ $\phantom{-}1$
47 $[47, 47, -w^{2} + 2]$ $\phantom{-}0$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 5]$ $\phantom{-}0$
47 $[47, 47, -\frac{3}{2}w^{3} + w^{2} + 10w + \frac{3}{2}]$ $\phantom{-}0$
47 $[47, 47, -\frac{1}{2}w^{3} + 5w - \frac{1}{2}]$ $\phantom{-}0$
67 $[67, 67, \frac{3}{2}w^{3} - 2w^{2} - 8w + \frac{3}{2}]$ $\phantom{-}4$
67 $[67, 67, \frac{1}{2}w^{3} - 2w - \frac{5}{2}]$ $\phantom{-}4$
67 $[67, 67, -\frac{1}{2}w^{3} + w^{2} + w - \frac{5}{2}]$ $\phantom{-}4$
67 $[67, 67, -\frac{3}{2}w^{3} + w^{2} + 9w - \frac{1}{2}]$ $\phantom{-}4$
81 $[81, 3, -3]$ $\phantom{-}18$
89 $[89, 89, w^{2} - 2w - 4]$ $\phantom{-}10$
89 $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - 9w + \frac{3}{2}]$ $\phantom{-}10$
89 $[89, 89, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{7}{2}]$ $\phantom{-}10$
89 $[89, 89, -w^{3} + 7w + 1]$ $\phantom{-}10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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