Base field 4.4.6224.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[29, 29, w^{2} - w - 1]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} - 21x^{10} + 159x^{8} - 519x^{6} + 688x^{4} - 364x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{4}e^{11} - 5e^{9} + \frac{141}{4}e^{7} - 102e^{5} + \frac{207}{2}e^{3} - 31e$ |
7 | $[7, 7, -w^{3} + w^{2} + 3w - 2]$ | $-\frac{1}{8}e^{11} + \frac{21}{8}e^{9} - \frac{159}{8}e^{7} + \frac{515}{8}e^{5} - \frac{161}{2}e^{3} + \frac{61}{2}e$ |
13 | $[13, 13, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{1}{2}e^{11} - \frac{41}{4}e^{9} + \frac{149}{2}e^{7} - \frac{897}{4}e^{5} + \frac{483}{2}e^{3} - 74e$ |
19 | $[19, 19, w^{3} - w^{2} - 5w + 2]$ | $-\frac{1}{4}e^{9} + \frac{7}{2}e^{7} - \frac{53}{4}e^{5} + 9e^{3} - 3e$ |
29 | $[29, 29, -w^{2} - w + 3]$ | $\phantom{-}\frac{3}{8}e^{11} - \frac{63}{8}e^{9} + \frac{469}{8}e^{7} - \frac{1437}{8}e^{5} + 192e^{3} - \frac{113}{2}e$ |
29 | $[29, 29, w^{2} - w - 1]$ | $-1$ |
37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{8}e^{11} - \frac{17}{8}e^{9} + \frac{95}{8}e^{7} - \frac{195}{8}e^{5} + 15e^{3} - \frac{7}{2}e$ |
37 | $[37, 37, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{1}{4}e^{10} - 6e^{8} + \frac{199}{4}e^{6} - 162e^{4} + 163e^{2} - 42$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 3w - 7]$ | $\phantom{-}\frac{1}{4}e^{11} - \frac{19}{4}e^{9} + \frac{125}{4}e^{7} - \frac{329}{4}e^{5} + \frac{147}{2}e^{3} - 24e$ |
47 | $[47, 47, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{1}{4}e^{10} + 5e^{8} - \frac{143}{4}e^{6} + 109e^{4} - 129e^{2} + 44$ |
47 | $[47, 47, 2w^{3} - 3w^{2} - 8w + 6]$ | $\phantom{-}\frac{1}{2}e^{10} - \frac{21}{2}e^{8} + 78e^{6} - 236e^{4} + 238e^{2} - 60$ |
59 | $[59, 59, -2w^{3} + w^{2} + 7w - 3]$ | $\phantom{-}\frac{3}{8}e^{11} - \frac{59}{8}e^{9} + \frac{401}{8}e^{7} - \frac{1057}{8}e^{5} + \frac{191}{2}e^{3} - \frac{11}{2}e$ |
67 | $[67, 67, w^{3} - 2w^{2} - 3w + 1]$ | $-\frac{1}{2}e^{10} + 11e^{8} - \frac{171}{2}e^{6} + 271e^{4} - 292e^{2} + 84$ |
73 | $[73, 73, -2w - 1]$ | $-\frac{3}{8}e^{11} + \frac{59}{8}e^{9} - \frac{401}{8}e^{7} + \frac{1053}{8}e^{5} - 92e^{3} + \frac{13}{2}e$ |
79 | $[79, 79, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{1}{4}e^{11} - \frac{21}{4}e^{9} + \frac{159}{4}e^{7} - \frac{515}{4}e^{5} + 159e^{3} - 51e$ |
81 | $[81, 3, -3]$ | $\phantom{-}2e^{2} - 6$ |
97 | $[97, 97, -3w + 2]$ | $\phantom{-}\frac{1}{4}e^{11} - \frac{21}{4}e^{9} + \frac{157}{4}e^{7} - \frac{487}{4}e^{5} + \frac{267}{2}e^{3} - 42e$ |
101 | $[101, 101, w^{3} - 3w^{2} - w + 4]$ | $\phantom{-}\frac{1}{2}e^{10} - \frac{19}{2}e^{8} + 64e^{6} - 183e^{4} + 206e^{2} - 70$ |
101 | $[101, 101, 2w^{3} - w^{2} - 9w + 1]$ | $-\frac{3}{4}e^{10} + \frac{31}{2}e^{8} - \frac{451}{4}e^{6} + 333e^{4} - 333e^{2} + 98$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29, 29, w^{2} - w - 1]$ | $1$ |