Properties

Label 2.2.221.1-5.1-c
Base field \(\Q(\sqrt{221}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, w]$
Dimension $4$
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: $4$
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:

\(x^{4} + x^{3} - 9x^{2} + x + 11\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w]$ $-1$
5 $[5, 5, w + 4]$ $\phantom{-}e^{3} + 3e^{2} - 4e - 6$
7 $[7, 7, w + 2]$ $-e^{3} - 2e^{2} + 6e + 4$
7 $[7, 7, w + 4]$ $\phantom{-}e^{3} + 3e^{2} - 5e - 7$
9 $[9, 3, 3]$ $-e^{3} - 2e^{2} + 5e + 2$
11 $[11, 11, w]$ $-2e^{3} - 5e^{2} + 10e + 12$
11 $[11, 11, w + 10]$ $-e + 1$
13 $[13, 13, w + 6]$ $\phantom{-}3e^{3} + 8e^{2} - 13e - 16$
17 $[17, 17, -w - 8]$ $-4e^{3} - 10e^{2} + 19e + 21$
31 $[31, 31, w + 14]$ $-4e^{3} - 10e^{2} + 19e + 23$
31 $[31, 31, w + 16]$ $\phantom{-}2e^{3} + 5e^{2} - 9e - 10$
37 $[37, 37, w + 15]$ $-4e^{3} - 11e^{2} + 18e + 24$
37 $[37, 37, w + 21]$ $\phantom{-}4e^{3} + 13e^{2} - 14e - 31$
41 $[41, 41, w + 18]$ $\phantom{-}4e^{3} + 9e^{2} - 20e - 14$
41 $[41, 41, w + 22]$ $-9e^{3} - 24e^{2} + 40e + 52$
43 $[43, 43, -w - 3]$ $\phantom{-}3e^{3} + 10e^{2} - 10e - 24$
43 $[43, 43, w - 4]$ $-e^{2} - 4e + 9$
53 $[53, 53, -w - 1]$ $\phantom{-}7e^{3} + 18e^{2} - 31e - 36$
53 $[53, 53, w - 2]$ $-4e^{3} - 10e^{2} + 18e + 19$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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