Properties

Label 2.2.221.1-5.1-e
Base field \(\Q(\sqrt{221}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, w]$
Dimension $6$
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: $6$
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:

\(x^{6} + 10x^{4} + 17x^{2} + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-\frac{1}{13}e^{4} - e^{2} - \frac{30}{13}$
5 $[5, 5, w]$ $\phantom{-}\frac{4}{13}e^{5} + 3e^{3} + \frac{55}{13}e$
5 $[5, 5, w + 4]$ $\phantom{-}e$
7 $[7, 7, w + 2]$ $-\frac{6}{13}e^{5} - 4e^{3} - \frac{37}{13}e$
7 $[7, 7, w + 4]$ $-\frac{10}{13}e^{5} - 7e^{3} - \frac{118}{13}e$
9 $[9, 3, 3]$ $-\frac{4}{13}e^{4} - 2e^{2} + \frac{10}{13}$
11 $[11, 11, w]$ $-\frac{2}{13}e^{5} - 2e^{3} - \frac{73}{13}e$
11 $[11, 11, w + 10]$ $-\frac{16}{13}e^{5} - 13e^{3} - \frac{337}{13}e$
13 $[13, 13, w + 6]$ $-\frac{1}{13}e^{4} + \frac{48}{13}$
17 $[17, 17, -w - 8]$ $-\frac{1}{13}e^{4} - e^{2} - \frac{30}{13}$
31 $[31, 31, w + 14]$ $\phantom{-}e$
31 $[31, 31, w + 16]$ $-\frac{15}{13}e^{5} - 11e^{3} - \frac{216}{13}e$
37 $[37, 37, w + 15]$ $\phantom{-}\frac{37}{13}e^{5} + 28e^{3} + \frac{603}{13}e$
37 $[37, 37, w + 21]$ $-\frac{3}{13}e^{5} - e^{3} + \frac{92}{13}e$
41 $[41, 41, w + 18]$ $-\frac{1}{13}e^{5} - 2e^{3} - \frac{95}{13}e$
41 $[41, 41, w + 22]$ $\phantom{-}\frac{7}{13}e^{5} + 6e^{3} + \frac{158}{13}e$
43 $[43, 43, -w - 3]$ $-\frac{5}{13}e^{4} - 4e^{2} + \frac{58}{13}$
43 $[43, 43, w - 4]$ $\phantom{-}\frac{8}{13}e^{4} + 6e^{2} + \frac{58}{13}$
53 $[53, 53, -w - 1]$ $-\frac{2}{13}e^{4} - e^{2} - \frac{34}{13}$
53 $[53, 53, w - 2]$ $\phantom{-}\frac{11}{13}e^{4} + 9e^{2} + \frac{135}{13}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w]$ $-\frac{4}{13}e^{5} - 3e^{3} - \frac{55}{13}e$