Properties

Label 2.2.56.1-11.2-a
Base field \(\Q(\sqrt{14}) \)
Weight $[2, 2]$
Level norm $11$
Level $[11,11,-w + 5]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\sqrt{14}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 14\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[11,11,-w + 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{4} - 4x^{2} + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 4]$ $\phantom{-}e^{2} - 1$
5 $[5, 5, -w + 3]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $\phantom{-}e^{3} - 5e$
7 $[7, 7, -2w - 7]$ $\phantom{-}2e^{3} - 7e$
9 $[9, 3, 3]$ $\phantom{-}0$
11 $[11, 11, w + 5]$ $\phantom{-}2$
11 $[11, 11, -w + 5]$ $-1$
13 $[13, 13, -w - 1]$ $\phantom{-}4e^{3} - 11e$
13 $[13, 13, -w + 1]$ $-3e^{3} + 10e$
31 $[31, 31, 2w - 5]$ $\phantom{-}2e$
31 $[31, 31, -2w - 5]$ $-e^{3} + e$
43 $[43, 43, 7w + 27]$ $\phantom{-}e^{2} + 2$
43 $[43, 43, 3w + 13]$ $-5e^{2} + 10$
47 $[47, 47, 2w - 3]$ $-2e^{3} + 10e$
47 $[47, 47, -2w - 3]$ $-4e^{3} + 15e$
61 $[61, 61, 7w + 25]$ $-5e^{3} + 13e$
61 $[61, 61, -5w - 17]$ $-7e^{3} + 18e$
67 $[67, 67, -w - 9]$ $\phantom{-}3e^{2} - 6$
67 $[67, 67, w - 9]$ $\phantom{-}2e^{2}$
101 $[101, 101, 3w - 5]$ $-3e^{3} + 4e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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