Properties

Label 2.2.316.1-5.2-a
Base field \(\Q(\sqrt{79}) \)
Weight $[2, 2]$
Level norm $5$
Level $[5,5,-w + 2]$
Dimension $6$
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: $6$
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:

\(x^{6} - 22x^{4} + 153x^{2} - 338\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 9]$ $\phantom{-}1$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{2}{13}e^{5} - \frac{31}{13}e^{3} + \frac{111}{13}e$
5 $[5, 5, w + 2]$ $\phantom{-}e^{2} - 8$
5 $[5, 5, w + 3]$ $-1$
7 $[7, 7, w + 3]$ $\phantom{-}\frac{3}{13}e^{5} - \frac{53}{13}e^{3} + \frac{212}{13}e$
7 $[7, 7, w + 4]$ $-\frac{3}{13}e^{5} + \frac{53}{13}e^{3} - \frac{212}{13}e$
13 $[13, 13, w + 1]$ $-e^{4} + 16e^{2} - 58$
13 $[13, 13, w + 12]$ $\phantom{-}e^{4} - 15e^{2} + 52$
43 $[43, 43, -w - 6]$ $\phantom{-}\frac{8}{13}e^{5} - \frac{124}{13}e^{3} + \frac{457}{13}e$
43 $[43, 43, w - 6]$ $-\frac{6}{13}e^{5} + \frac{93}{13}e^{3} - \frac{333}{13}e$
47 $[47, 47, w + 19]$ $\phantom{-}\frac{5}{13}e^{5} - \frac{84}{13}e^{3} + \frac{336}{13}e$
47 $[47, 47, w + 28]$ $\phantom{-}\frac{7}{13}e^{5} - \frac{115}{13}e^{3} + \frac{434}{13}e$
59 $[59, 59, w + 16]$ $-\frac{6}{13}e^{5} + \frac{93}{13}e^{3} - \frac{333}{13}e$
59 $[59, 59, w + 43]$ $\phantom{-}\frac{3}{13}e^{5} - \frac{53}{13}e^{3} + \frac{251}{13}e$
71 $[71, 71, w + 24]$ $-\frac{5}{13}e^{5} + \frac{58}{13}e^{3} - \frac{102}{13}e$
71 $[71, 71, w + 47]$ $\phantom{-}e^{3} - 8e$
73 $[73, 73, 3w - 28]$ $\phantom{-}e^{4} - 12e^{2} + 32$
73 $[73, 73, 12w - 107]$ $-e^{4} + 19e^{2} - 78$
79 $[79, 79, -w]$ $-\frac{9}{13}e^{5} + \frac{133}{13}e^{3} - \frac{454}{13}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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