Properties

Base field \(\Q(\sqrt{165}) \)
Weight [2, 2]
Level norm 33
Level $[33, 33, w + 16]$
Label 2.2.165.1-33.1-a
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{165}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 41\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[33, 33, w + 16]$
Label 2.2.165.1-33.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 156

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
4 $[4, 2, 2]$ $-3$
5 $[5, 5, w + 2]$ $-2$
7 $[7, 7, w + 2]$ $\phantom{-}4$
7 $[7, 7, w + 4]$ $\phantom{-}4$
11 $[11, 11, w + 5]$ $\phantom{-}1$
13 $[13, 13, w + 1]$ $-2$
13 $[13, 13, w + 11]$ $-2$
23 $[23, 23, w + 10]$ $\phantom{-}8$
23 $[23, 23, w + 12]$ $\phantom{-}8$
29 $[29, 29, -w - 3]$ $-6$
29 $[29, 29, w - 4]$ $-6$
31 $[31, 31, -w - 8]$ $-8$
31 $[31, 31, w - 9]$ $-8$
41 $[41, 41, -w]$ $-2$
41 $[41, 41, w - 1]$ $-2$
43 $[43, 43, w + 18]$ $\phantom{-}0$
43 $[43, 43, w + 24]$ $\phantom{-}0$
47 $[47, 47, w + 13]$ $\phantom{-}8$
47 $[47, 47, w + 33]$ $\phantom{-}8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $1$
11 $[11, 11, w + 5]$ $-1$