Properties

Base field \(\Q(\sqrt{11}) \)
Weight [2, 2]
Level norm 441
Level $[441, 21, 21]$
Label 2.2.44.1-441.1-k
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{11}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 11\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[441, 21, 21]$
Label 2.2.44.1-441.1-k
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 170

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 3]$ $-1$
5 $[5, 5, w - 4]$ $-2$
5 $[5, 5, -w - 4]$ $-2$
7 $[7, 7, w + 2]$ $-1$
7 $[7, 7, w - 2]$ $-1$
9 $[9, 3, 3]$ $\phantom{-}1$
11 $[11, 11, -w]$ $\phantom{-}4$
19 $[19, 19, 2w - 5]$ $\phantom{-}4$
19 $[19, 19, -2w - 5]$ $\phantom{-}4$
37 $[37, 37, 2w - 9]$ $\phantom{-}6$
37 $[37, 37, -2w - 9]$ $\phantom{-}6$
43 $[43, 43, 2w - 1]$ $-4$
43 $[43, 43, -2w - 1]$ $-4$
53 $[53, 53, -w - 8]$ $\phantom{-}6$
53 $[53, 53, w - 8]$ $\phantom{-}6$
79 $[79, 79, 5w - 14]$ $-16$
79 $[79, 79, 8w - 25]$ $-16$
83 $[83, 83, -3w - 4]$ $-12$
83 $[83, 83, 3w - 4]$ $-12$
89 $[89, 89, -w - 10]$ $-14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w + 2]$ $1$
7 $[7, 7, w - 2]$ $1$
9 $[9, 3, 3]$ $-1$