Properties

Label 2.2.181.1-11.2-a
Base field \(\Q(\sqrt{181}) \)
Weight $[2, 2]$
Level norm $11$
Level $[11,11,-w - 7]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{181}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[11,11,-w - 7]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $42$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} + x - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 6]$ $-1$
3 $[3, 3, -w + 7]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-e$
5 $[5, 5, 4w + 25]$ $\phantom{-}0$
5 $[5, 5, -4w + 29]$ $\phantom{-}e - 2$
11 $[11, 11, w - 8]$ $-e - 4$
11 $[11, 11, -w - 7]$ $-1$
13 $[13, 13, 3w + 19]$ $-1$
13 $[13, 13, 3w - 22]$ $-e - 2$
29 $[29, 29, 6w + 37]$ $\phantom{-}3e$
29 $[29, 29, 6w - 43]$ $-e - 7$
37 $[37, 37, 2w - 13]$ $-2e + 2$
37 $[37, 37, 2w + 11]$ $\phantom{-}3e - 5$
43 $[43, 43, -w - 1]$ $\phantom{-}e - 6$
43 $[43, 43, w - 2]$ $\phantom{-}e - 6$
49 $[49, 7, -7]$ $\phantom{-}2e - 5$
59 $[59, 59, 5w - 37]$ $-e + 2$
59 $[59, 59, 5w + 32]$ $-3e$
67 $[67, 67, 21w + 131]$ $-3e - 5$
67 $[67, 67, 21w - 152]$ $\phantom{-}e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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