Properties

Label 2.2.33.1-588.1-e
Base field \(\Q(\sqrt{33}) \)
Weight $[2, 2]$
Level norm $588$
Level $[588, 42, -28w + 98]$
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: $[588, 42, -28w + 98]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $46$

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w - 2]$ $-1$
$2$ $[2, 2, -w + 3]$ $-1$
$3$ $[3, 3, 2w - 7]$ $1$
$49$ $[49, 7, -7]$ $-1$