Properties

Label 2.2.17.1-16.1-a
Base field \(\Q(\sqrt{17}) \)
Weight $[2, 2]$
Level norm $16$
Level $[16, 4, 4]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\sqrt{17}) \)

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

Form

Weight: $[2, 2]$
Level: $[16, 4, 4]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $1$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}0$
2 $[2, 2, -w - 1]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}4$
13 $[13, 13, -2w + 3]$ $-4$
13 $[13, 13, 2w + 1]$ $-4$
17 $[17, 17, -2w + 1]$ $\phantom{-}6$
19 $[19, 19, -2w + 7]$ $-4$
19 $[19, 19, 2w + 5]$ $-4$
25 $[25, 5, -5]$ $\phantom{-}2$
43 $[43, 43, 4w - 7]$ $\phantom{-}8$
43 $[43, 43, 4w + 3]$ $\phantom{-}8$
47 $[47, 47, -2w + 9]$ $-12$
47 $[47, 47, 2w + 7]$ $-12$
49 $[49, 7, -7]$ $-4$
53 $[53, 53, 4w - 13]$ $-6$
53 $[53, 53, 6w - 13]$ $-6$
59 $[59, 59, -4w - 1]$ $\phantom{-}0$
59 $[59, 59, 4w - 5]$ $\phantom{-}0$
67 $[67, 67, 4w - 3]$ $-4$
67 $[67, 67, 4w - 1]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 2]$ $-1$
$2$ $[2, 2, -w - 1]$ $-1$