Properties

Label 2.2.221.1-13.1-f
Base field \(\Q(\sqrt{221}) \)
Weight $[2, 2]$
Level norm $13$
Level $[13, 13, w + 6]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{221}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[13, 13, w + 6]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $132$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}0$
5 $[5, 5, w + 4]$ $\phantom{-}e$
7 $[7, 7, w + 2]$ $\phantom{-}0$
7 $[7, 7, w + 4]$ $\phantom{-}0$
9 $[9, 3, 3]$ $-2$
11 $[11, 11, w]$ $-e$
11 $[11, 11, w + 10]$ $-e$
13 $[13, 13, w + 6]$ $\phantom{-}1$
17 $[17, 17, -w - 8]$ $\phantom{-}6$
31 $[31, 31, w + 14]$ $\phantom{-}e$
31 $[31, 31, w + 16]$ $-e$
37 $[37, 37, w + 15]$ $-2e$
37 $[37, 37, w + 21]$ $-e$
41 $[41, 41, w + 18]$ $\phantom{-}3e$
41 $[41, 41, w + 22]$ $\phantom{-}0$
43 $[43, 43, -w - 3]$ $\phantom{-}4$
43 $[43, 43, w - 4]$ $-8$
53 $[53, 53, -w - 1]$ $-6$
53 $[53, 53, w - 2]$ $-6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13, 13, w + 6]$ $-1$