Base field \(\Q(\sqrt{389}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 97\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 2, 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 3x^{5} - 18x^{4} + 41x^{3} + 90x^{2} - 111x - 163\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, -3w - 28]$ | $-e + 1$ |
5 | $[5, 5, -3w + 31]$ | $\phantom{-}e$ |
7 | $[7, 7, -w - 9]$ | $-\frac{1}{6}e^{5} + \frac{1}{2}e^{4} + \frac{7}{3}e^{3} - \frac{11}{2}e^{2} - \frac{29}{6}e + \frac{26}{3}$ |
7 | $[7, 7, -w + 10]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{1}{3}e^{4} - \frac{8}{3}e^{3} + \frac{17}{6}e^{2} + \frac{23}{3}e + 1$ |
9 | $[9, 3, 3]$ | $-\frac{1}{12}e^{4} + \frac{1}{6}e^{3} + \frac{19}{12}e^{2} - \frac{5}{3}e - \frac{103}{12}$ |
11 | $[11, 11, -2w - 19]$ | $-\frac{1}{12}e^{5} + \frac{1}{6}e^{4} + \frac{19}{12}e^{3} - \frac{5}{3}e^{2} - \frac{79}{12}e + 2$ |
11 | $[11, 11, 2w - 21]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{1}{4}e^{4} - \frac{17}{12}e^{3} + \frac{13}{4}e^{2} + \frac{59}{12}e - \frac{55}{12}$ |
13 | $[13, 13, w - 11]$ | $-\frac{1}{12}e^{5} + \frac{23}{12}e^{3} + e^{2} - \frac{113}{12}e - \frac{20}{3}$ |
13 | $[13, 13, -w - 10]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{5}{12}e^{4} - \frac{13}{12}e^{3} + \frac{71}{12}e^{2} + \frac{25}{12}e - \frac{53}{4}$ |
17 | $[17, 17, -8w - 75]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{5}{12}e^{4} - \frac{13}{12}e^{3} + \frac{71}{12}e^{2} + \frac{25}{12}e - \frac{49}{4}$ |
17 | $[17, 17, -8w + 83]$ | $-\frac{1}{12}e^{5} + \frac{23}{12}e^{3} + e^{2} - \frac{113}{12}e - \frac{17}{3}$ |
19 | $[19, 19, -5w + 52]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{17}{4}e^{2} + \frac{11}{2}e + \frac{57}{4}$ |
19 | $[19, 19, 5w + 47]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{3} - \frac{17}{4}e^{2} + \frac{7}{2}e + \frac{61}{4}$ |
41 | $[41, 41, -w - 7]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{15}{4}e^{3} + 4e^{2} + \frac{35}{4}e + 4$ |
41 | $[41, 41, w - 8]$ | $-\frac{1}{4}e^{5} + \frac{3}{4}e^{4} + \frac{13}{4}e^{3} - \frac{31}{4}e^{2} - \frac{19}{4}e + \frac{51}{4}$ |
59 | $[59, 59, -w - 12]$ | $-\frac{1}{6}e^{5} + \frac{23}{6}e^{3} + \frac{5}{2}e^{2} - \frac{55}{3}e - \frac{95}{6}$ |
59 | $[59, 59, w - 13]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{5}{6}e^{4} - \frac{13}{6}e^{3} + \frac{37}{3}e^{2} + \frac{8}{3}e - 28$ |
67 | $[67, 67, -w - 5]$ | $\phantom{-}\frac{1}{6}e^{5} + \frac{1}{6}e^{4} - \frac{25}{6}e^{3} - \frac{25}{6}e^{2} + \frac{121}{6}e + \frac{33}{2}$ |
67 | $[67, 67, w - 6]$ | $-\frac{1}{6}e^{5} + e^{4} + \frac{11}{6}e^{3} - 14e^{2} - \frac{5}{6}e + \frac{86}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $1$ |