Properties

Base field \(\Q(\sqrt{89}) \)
Weight [2, 2]
Level norm 81
Level $[81, 9, 9]$
Label 2.2.89.1-81.1-a
Dimension 1
CM yes
Base change yes

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{89}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 22\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[81, 9, 9]$
Label 2.2.89.1-81.1-a
Dimension 1
Is CM yes
Is base change yes
Parent newspace dimension 152

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w - 4]$ $\phantom{-}0$
2 $[2, 2, -w + 5]$ $\phantom{-}0$
5 $[5, 5, 4w - 21]$ $\phantom{-}0$
5 $[5, 5, -4w - 17]$ $\phantom{-}0$
9 $[9, 3, 3]$ $\phantom{-}0$
11 $[11, 11, 2w - 11]$ $\phantom{-}0$
11 $[11, 11, -2w - 9]$ $\phantom{-}0$
17 $[17, 17, -6w - 25]$ $\phantom{-}0$
17 $[17, 17, -6w + 31]$ $\phantom{-}0$
47 $[47, 47, 24w + 101]$ $\phantom{-}0$
47 $[47, 47, 24w - 125]$ $\phantom{-}0$
49 $[49, 7, -7]$ $\phantom{-}14$
53 $[53, 53, 2w - 7]$ $\phantom{-}0$
53 $[53, 53, -2w - 5]$ $\phantom{-}0$
67 $[67, 67, 4w - 19]$ $-1$
67 $[67, 67, 4w + 15]$ $-1$
71 $[71, 71, 16w - 83]$ $\phantom{-}0$
71 $[71, 71, 16w + 67]$ $\phantom{-}0$
73 $[73, 73, 2w - 5]$ $\phantom{-}5$
73 $[73, 73, -2w - 3]$ $\phantom{-}5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, 3]$ $1$