Properties

Label 2.2.221.1-7.2-b
Base field \(\Q(\sqrt{221}) \)
Weight $[2, 2]$
Level norm $7$
Level $[7,7,-w + 3]$
Dimension $15$
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: $[7,7,-w + 3]$
Dimension: $15$
CM: no
Base change: no
Newspace dimension: $60$

Hecke eigenvalues ($q$-expansion)

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

\(x^{15} + 4x^{14} - 26x^{13} - 114x^{12} + 221x^{11} + 1184x^{10} - 551x^{9} - 5490x^{8} - 1181x^{7} + 11353x^{6} + 6350x^{5} - 9474x^{4} - 6955x^{3} + 2503x^{2} + 2130x + 25\)

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

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7,7,-w + 3]$ $-1$