Properties

Label 2.2.44.1-392.1-d
Base field \(\Q(\sqrt{11}) \)
Weight $[2, 2]$
Level norm $392$
Level $[392, 28, -14w + 42]$
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: $[392, 28, -14w + 42]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $56$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 3]$ $\phantom{-}0$
5 $[5, 5, w - 4]$ $-4$
5 $[5, 5, -w - 4]$ $-4$
7 $[7, 7, w + 2]$ $\phantom{-}1$
7 $[7, 7, w - 2]$ $\phantom{-}1$
9 $[9, 3, 3]$ $-2$
11 $[11, 11, -w]$ $\phantom{-}0$
19 $[19, 19, 2w - 5]$ $-2$
19 $[19, 19, -2w - 5]$ $-2$
37 $[37, 37, 2w - 9]$ $-6$
37 $[37, 37, -2w - 9]$ $-6$
43 $[43, 43, 2w - 1]$ $\phantom{-}8$
43 $[43, 43, -2w - 1]$ $\phantom{-}8$
53 $[53, 53, -w - 8]$ $-10$
53 $[53, 53, w - 8]$ $-10$
79 $[79, 79, 5w - 14]$ $-8$
79 $[79, 79, 8w - 25]$ $-8$
83 $[83, 83, -3w - 4]$ $\phantom{-}6$
83 $[83, 83, 3w - 4]$ $\phantom{-}6$
89 $[89, 89, -w - 10]$ $\phantom{-}10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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