Properties

Base field \(\Q(\sqrt{33}) \)
Weight [2, 2]
Level norm 192
Level $[192, 24, 16w - 56]$
Label 2.2.33.1-192.1-f
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{33}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 8\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[192, 24, 16w - 56]$
Label 2.2.33.1-192.1-f
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
2 $[2, 2, -w + 3]$ $\phantom{-}0$
3 $[3, 3, 2w - 7]$ $-1$
11 $[11, 11, 4w - 13]$ $\phantom{-}4$
17 $[17, 17, -2w + 5]$ $\phantom{-}2$
17 $[17, 17, 2w + 3]$ $\phantom{-}2$
25 $[25, 5, 5]$ $-6$
29 $[29, 29, -2w + 3]$ $\phantom{-}6$
29 $[29, 29, 2w + 1]$ $\phantom{-}6$
31 $[31, 31, -2w + 9]$ $\phantom{-}8$
31 $[31, 31, 2w + 7]$ $\phantom{-}8$
37 $[37, 37, -4w - 11]$ $\phantom{-}6$
37 $[37, 37, 4w - 15]$ $\phantom{-}6$
41 $[41, 41, -10w + 33]$ $-6$
41 $[41, 41, 6w - 19]$ $-6$
49 $[49, 7, -7]$ $-14$
67 $[67, 67, 2w - 11]$ $-4$
67 $[67, 67, -2w - 9]$ $-4$
83 $[83, 83, 4w + 5]$ $-4$
83 $[83, 83, 4w - 9]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
2 $[2, 2, -w + 3]$ $-1$
3 $[3, 3, 2w - 7]$ $1$