Properties

Label 2.2.316.1-4.1-b
Base field \(\Q(\sqrt{79}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 2, 2]$
Dimension $8$
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: $[4, 2, 2]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $42$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 16x^{6} + 54x^{4} - 16x^{2} + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 9]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $-e^{7} + 16e^{5} - 54e^{3} + 16e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{47}{4}e^{4} + \frac{149}{4}e^{2} - \frac{21}{4}$
5 $[5, 5, w + 3]$ $-\frac{3}{4}e^{6} + \frac{47}{4}e^{4} - \frac{149}{4}e^{2} + \frac{21}{4}$
7 $[7, 7, w + 3]$ $\phantom{-}\frac{9}{4}e^{7} - \frac{143}{4}e^{5} + \frac{471}{4}e^{3} - \frac{101}{4}e$
7 $[7, 7, w + 4]$ $-\frac{5}{4}e^{7} + \frac{79}{4}e^{5} - \frac{255}{4}e^{3} + \frac{33}{4}e$
13 $[13, 13, w + 1]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{47}{4}e^{4} + \frac{145}{4}e^{2} - \frac{9}{4}$
13 $[13, 13, w + 12]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{17}{4}e^{4} + \frac{67}{4}e^{2} - \frac{31}{4}$
43 $[43, 43, -w - 6]$ $\phantom{-}2e^{7} - \frac{63}{2}e^{5} + 101e^{3} - \frac{31}{2}e$
43 $[43, 43, w - 6]$ $-\frac{11}{2}e^{7} + 87e^{5} - \frac{563}{2}e^{3} + 40e$
47 $[47, 47, w + 19]$ $\phantom{-}\frac{23}{4}e^{7} - \frac{367}{4}e^{5} + \frac{1221}{4}e^{3} - \frac{265}{4}e$
47 $[47, 47, w + 28]$ $\phantom{-}\frac{31}{4}e^{7} - \frac{491}{4}e^{5} + \frac{1593}{4}e^{3} - \frac{233}{4}e$
59 $[59, 59, w + 16]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{17}{2}e^{5} + \frac{69}{2}e^{3} - \frac{59}{2}e$
59 $[59, 59, w + 43]$ $\phantom{-}\frac{5}{2}e^{7} - \frac{79}{2}e^{5} + \frac{255}{2}e^{3} - \frac{43}{2}e$
71 $[71, 71, w + 24]$ $-\frac{19}{4}e^{7} + \frac{301}{4}e^{5} - \frac{981}{4}e^{3} + \frac{183}{4}e$
71 $[71, 71, w + 47]$ $\phantom{-}\frac{7}{4}e^{7} - \frac{109}{4}e^{5} + \frac{333}{4}e^{3} + \frac{21}{4}e$
73 $[73, 73, 3w - 28]$ $\phantom{-}2e^{6} - \frac{63}{2}e^{4} + 102e^{2} - \frac{33}{2}$
73 $[73, 73, 12w - 107]$ $-2e^{6} + \frac{63}{2}e^{4} - 102e^{2} + \frac{41}{2}$
79 $[79, 79, -w]$ $\phantom{-}\frac{13}{2}e^{7} - \frac{207}{2}e^{5} + \frac{685}{2}e^{3} - \frac{151}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 9]$ $-1$