Properties

Label 2.2.221.1-5.1-a
Base field \(\Q(\sqrt{221}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, w]$
Dimension $3$
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: $[5, 5, w]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 2x^{2} - x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}1$
5 $[5, 5, w + 4]$ $\phantom{-}e + 2$
7 $[7, 7, w + 2]$ $\phantom{-}2e^{2} + 3e - 4$
7 $[7, 7, w + 4]$ $-2e^{2} - 5e + 1$
9 $[9, 3, 3]$ $-2e^{2} - 4e + 2$
11 $[11, 11, w]$ $-2e^{2} - 3e + 2$
11 $[11, 11, w + 10]$ $\phantom{-}4e^{2} + 4e - 5$
13 $[13, 13, w + 6]$ $\phantom{-}e^{2} + 3e - 2$
17 $[17, 17, -w - 8]$ $\phantom{-}e$
31 $[31, 31, w + 14]$ $-e - 2$
31 $[31, 31, w + 16]$ $-e^{2} - 4e$
37 $[37, 37, w + 15]$ $-e^{2} + 4e + 3$
37 $[37, 37, w + 21]$ $\phantom{-}5e^{2} + 6e - 10$
41 $[41, 41, w + 18]$ $-5e^{2} - 10e + 1$
41 $[41, 41, w + 22]$ $-3e^{2} - 5e + 1$
43 $[43, 43, -w - 3]$ $\phantom{-}e^{2} - e - 12$
43 $[43, 43, w - 4]$ $-2e^{2} + 6$
53 $[53, 53, -w - 1]$ $\phantom{-}e^{2} + 2e + 2$
53 $[53, 53, w - 2]$ $-2e^{2} + 3e + 7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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