Properties

Base field \(\Q(\sqrt{161}) \)
Weight [2, 2]
Level norm 28
Level $[28, 14, 64w - 438]$
Label 2.2.161.1-28.1-b
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{161}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 40\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[28, 14, 64w - 438]$
Label 2.2.161.1-28.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w + 6]$ $-1$
2 $[2, 2, -w + 7]$ $-1$
5 $[5, 5, -6w - 35]$ $\phantom{-}0$
5 $[5, 5, -6w + 41]$ $\phantom{-}0$
7 $[7, 7, 32w - 219]$ $\phantom{-}1$
9 $[9, 3, 3]$ $-2$
17 $[17, 17, 2w - 13]$ $\phantom{-}6$
17 $[17, 17, 2w + 11]$ $\phantom{-}6$
19 $[19, 19, 4w + 23]$ $\phantom{-}2$
19 $[19, 19, 4w - 27]$ $\phantom{-}2$
23 $[23, 23, 58w - 397]$ $\phantom{-}0$
29 $[29, 29, 20w - 137]$ $-6$
29 $[29, 29, -20w - 117]$ $-6$
61 $[61, 61, 2w - 11]$ $\phantom{-}8$
61 $[61, 61, -2w - 9]$ $\phantom{-}8$
71 $[71, 71, -10w - 59]$ $\phantom{-}0$
71 $[71, 71, 10w - 69]$ $\phantom{-}0$
83 $[83, 83, -44w + 301]$ $-6$
83 $[83, 83, 44w + 257]$ $-6$
89 $[89, 89, -70w - 409]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 6]$ $1$
2 $[2, 2, -w + 7]$ $1$
7 $[7, 7, 32w - 219]$ $-1$