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 | $[79, 79, -w]$ | $\phantom{-}\frac{13}{2}e^{7} - \frac{207}{2}e^{5} + \frac{685}{2}e^{3} - \frac{151}{2}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 9]$ | $-1$ |