Properties

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

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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: $6$
CM: no
Base change: yes
Newspace dimension: $132$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} + 18x^{4} + 15x^{2} + 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{17}{2}e^{2} + 2$
5 $[5, 5, w]$ $\phantom{-}e$
5 $[5, 5, w + 4]$ $\phantom{-}e$
7 $[7, 7, w + 2]$ $\phantom{-}\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + \frac{17}{3}e$
7 $[7, 7, w + 4]$ $\phantom{-}\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + \frac{17}{3}e$
9 $[9, 3, 3]$ $-\frac{5}{6}e^{4} - \frac{89}{6}e^{2} - \frac{13}{3}$
11 $[11, 11, w]$ $-\frac{1}{2}e^{5} - \frac{17}{2}e^{3} + e$
11 $[11, 11, w + 10]$ $-\frac{1}{2}e^{5} - \frac{17}{2}e^{3} + e$
13 $[13, 13, w + 6]$ $\phantom{-}1$
17 $[17, 17, -w - 8]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{19}{3}e^{2} + \frac{16}{3}$
31 $[31, 31, w + 14]$ $\phantom{-}2e^{5} + 35e^{3} + 14e$
31 $[31, 31, w + 16]$ $\phantom{-}2e^{5} + 35e^{3} + 14e$
37 $[37, 37, w + 15]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{19}{3}e^{3} + \frac{25}{3}e$
37 $[37, 37, w + 21]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{19}{3}e^{3} + \frac{25}{3}e$
41 $[41, 41, w + 18]$ $\phantom{-}e^{5} + 18e^{3} + 15e$
41 $[41, 41, w + 22]$ $\phantom{-}e^{5} + 18e^{3} + 15e$
43 $[43, 43, -w - 3]$ $-2e^{4} - 35e^{2} - 18$
43 $[43, 43, w - 4]$ $-2e^{4} - 35e^{2} - 18$
53 $[53, 53, -w - 1]$ $-\frac{1}{2}e^{4} - \frac{19}{2}e^{2} - 11$
53 $[53, 53, w - 2]$ $-\frac{1}{2}e^{4} - \frac{19}{2}e^{2} - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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