Properties

Base field \(\Q(\sqrt{33}) \)
Weight [2, 2]
Level norm 11
Level $[11, 11, 4w - 13]$
Label 2.2.33.1-11.1-b
Dimension 1
CM no
Base change yes

Related objects

Downloads

Learn more about

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 $[11, 11, 4w - 13]$
Label 2.2.33.1-11.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 2

Hecke eigenvalues ($q$-expansion)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, 4w - 13]$ $-1$