Properties

Base field \(\Q(\sqrt{2}) \)
Weight [2, 2]
Level norm 89
Level $[89, 89, -4w - 11]$
Label 2.2.8.1-89.1-c
Dimension 2
CM no
Base change no

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Base field \(\Q(\sqrt{2}) \)

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

Form

Weight [2, 2]
Level $[89, 89, -4w - 11]$
Label 2.2.8.1-89.1-c
Dimension 2
Is CM no
Is base change no
Parent newspace dimension 4

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut 3x \) \(\mathstrut -\mathstrut 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}2$
7 $[7, 7, -2w + 1]$ $\phantom{-}e$
7 $[7, 7, -2w - 1]$ $-2e - 4$
9 $[9, 3, 3]$ $\phantom{-}2e + 2$
17 $[17, 17, 3w + 1]$ $-3e - 4$
17 $[17, 17, 3w - 1]$ $\phantom{-}e$
23 $[23, 23, w + 5]$ $-e - 4$
23 $[23, 23, -w + 5]$ $\phantom{-}2e + 4$
25 $[25, 5, 5]$ $-e + 4$
31 $[31, 31, 4w + 1]$ $-2e$
31 $[31, 31, -4w + 1]$ $\phantom{-}2e + 2$
41 $[41, 41, 2w - 7]$ $\phantom{-}e + 4$
41 $[41, 41, -2w - 7]$ $\phantom{-}10$
47 $[47, 47, -w - 7]$ $\phantom{-}2e + 2$
47 $[47, 47, w - 7]$ $-e - 4$
71 $[71, 71, -6w - 1]$ $-3e - 4$
71 $[71, 71, 6w - 1]$ $-2e - 2$
73 $[73, 73, -7w - 5]$ $-2e - 14$
73 $[73, 73, 7w - 5]$ $-4e - 10$
79 $[79, 79, -w - 9]$ $\phantom{-}5e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
89 $[89, 89, -4w - 11]$ $1$