Properties

Base field \(\Q(\sqrt{22}) \)
Weight [2, 2]
Level norm 121
Level $[121, 11, 11]$
Label 2.2.88.1-121.1-b
Dimension 1
CM no
Base change yes

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{22}) \)

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

Form

Weight [2, 2]
Level $[121, 11, 11]$
Label 2.2.88.1-121.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 209

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -3w + 14]$ $-1$
3 $[3, 3, -w + 5]$ $\phantom{-}2$
3 $[3, 3, w + 5]$ $\phantom{-}2$
7 $[7, 7, 2w + 9]$ $\phantom{-}2$
7 $[7, 7, 2w - 9]$ $\phantom{-}2$
11 $[11, 11, -7w + 33]$ $\phantom{-}0$
13 $[13, 13, -w - 3]$ $-1$
13 $[13, 13, -w + 3]$ $-1$
25 $[25, 5, -5]$ $-9$
29 $[29, 29, 3w + 13]$ $-9$
29 $[29, 29, -3w + 13]$ $-9$
59 $[59, 59, -w - 9]$ $\phantom{-}8$
59 $[59, 59, w - 9]$ $\phantom{-}8$
61 $[61, 61, 11w - 51]$ $-6$
61 $[61, 61, 25w - 117]$ $-6$
67 $[67, 67, 9w - 43]$ $\phantom{-}2$
67 $[67, 67, -9w - 43]$ $\phantom{-}2$
79 $[79, 79, 2w - 3]$ $\phantom{-}10$
79 $[79, 79, -2w - 3]$ $\phantom{-}10$
89 $[89, 89, 4w - 21]$ $-9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -7w + 33]$ $-1$