Properties

Label 2.2.316.1-5.1-e
Base field \(\Q(\sqrt{79}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5, 5, w + 2]$
Dimension $20$
CM no
Base change no

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Base field \(\Q(\sqrt{79}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[5, 5, w + 2]$
Dimension: $20$
CM: no
Base change: no
Newspace dimension: $150$

Hecke eigenvalues ($q$-expansion)

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

\(x^{20} - 38x^{18} + 578x^{16} - 4564x^{14} + 20458x^{12} - 53719x^{10} + 82626x^{8} - 72700x^{6} + 34125x^{4} - 7172x^{2} + 404\)

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Norm Prime Eigenvalue
2 $[2, 2, -w + 9]$ $...$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $...$
5 $[5, 5, w + 2]$ $\phantom{-}1$
5 $[5, 5, w + 3]$ $...$
7 $[7, 7, w + 3]$ $...$
7 $[7, 7, w + 4]$ $...$
13 $[13, 13, w + 1]$ $...$
13 $[13, 13, w + 12]$ $...$
43 $[43, 43, -w - 6]$ $...$
43 $[43, 43, w - 6]$ $...$
47 $[47, 47, w + 19]$ $...$
47 $[47, 47, w + 28]$ $...$
59 $[59, 59, w + 16]$ $...$
59 $[59, 59, w + 43]$ $...$
71 $[71, 71, w + 24]$ $...$
71 $[71, 71, w + 47]$ $...$
73 $[73, 73, 3w - 28]$ $...$
73 $[73, 73, 12w - 107]$ $...$
79 $[79, 79, -w]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w + 2]$ $-1$