Properties

Label 4.4.6224.1-29.2-e
Base field 4.4.6224.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29, 29, w^{2} - w - 1]$
Dimension $12$
CM no
Base change no

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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 $[101, 101, 2w^{3} - w^{2} - 9w + 1]$ $-\frac{3}{4}e^{10} + \frac{31}{2}e^{8} - \frac{451}{4}e^{6} + 333e^{4} - 333e^{2} + 98$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29, 29, w^{2} - w - 1]$ $1$